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Properties

Label 92400hj
Number of curves $8$
Conductor $92400$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("hj1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 92400hj have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(5\)\(1\)
\(7\)\(1 - T\)
\(11\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(13\) \( 1 - 7 T + 13 T^{2}\) 1.13.ah
\(17\) \( 1 - 6 T + 17 T^{2}\) 1.17.ag
\(19\) \( 1 - T + 19 T^{2}\) 1.19.ab
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 3 T + 29 T^{2}\) 1.29.d
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 92400hj do not have complex multiplication.

Modular form 92400.2.a.hj

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} + q^{11} - 2 q^{13} - 6 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.

Elliptic curves in class 92400hj

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.ho8 92400hj1 \([0, 1, 0, 635592, -24208812]\) \(443688652450511/260789760000\) \(-16690544640000000000\) \([2]\) \(1990656\) \(2.3778\) \(\Gamma_0(N)\)-optimal
92400.ho7 92400hj2 \([0, 1, 0, -2564408, -197008812]\) \(29141055407581489/16604321025600\) \(1062676545638400000000\) \([2, 2]\) \(3981312\) \(2.7244\)  
92400.ho6 92400hj3 \([0, 1, 0, -8100408, 9739951188]\) \(-918468938249433649/109183593750000\) \(-6987750000000000000000\) \([2]\) \(5971968\) \(2.9271\)  
92400.ho5 92400hj4 \([0, 1, 0, -26324408, 51742351188]\) \(31522423139920199089/164434491947880\) \(10523807484664320000000\) \([2]\) \(7962624\) \(3.0710\)  
92400.ho4 92400hj5 \([0, 1, 0, -30004408, -63144368812]\) \(46676570542430835889/106752955783320\) \(6832189170132480000000\) \([2]\) \(7962624\) \(3.0710\)  
92400.ho3 92400hj6 \([0, 1, 0, -133100408, 590989951188]\) \(4074571110566294433649/48828650062500\) \(3125033604000000000000\) \([2, 2]\) \(11943936\) \(3.2737\)  
92400.ho1 92400hj7 \([0, 1, 0, -2129600408, 37825714951188]\) \(16689299266861680229173649/2396798250\) \(153395088000000000\) \([2]\) \(23887872\) \(3.6203\)  
92400.ho2 92400hj8 \([0, 1, 0, -136600408, 558264951188]\) \(4404531606962679693649/444872222400201750\) \(28471822233612912000000000\) \([2]\) \(23887872\) \(3.6203\)