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Properties

Label 39326.m
Number of curves $6$
Conductor $39326$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("m1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 39326.m have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(7\)\(1 - T\)
\(53\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 - 2 T + 3 T^{2}\) 1.3.ac
\(5\) \( 1 + 5 T^{2}\) 1.5.a
\(11\) \( 1 + 11 T^{2}\) 1.11.a
\(13\) \( 1 + 4 T + 13 T^{2}\) 1.13.e
\(17\) \( 1 - 6 T + 17 T^{2}\) 1.17.ag
\(19\) \( 1 + 2 T + 19 T^{2}\) 1.19.c
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 39326.m do not have complex multiplication.

Modular form 39326.2.a.m

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} + q^{7} + q^{8} + q^{9} + 2 q^{12} - 4 q^{13} + q^{14} + q^{16} + 6 q^{17} + q^{18} - 2 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 39326.m

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39326.m1 39326l6 \([1, 1, 1, -7670033, -8179253777]\) \(2251439055699625/25088\) \(556059492004352\) \([2]\) \(898560\) \(2.3982\)  
39326.m2 39326l5 \([1, 1, 1, -478993, -128165393]\) \(-548347731625/1835008\) \(-40671779986604032\) \([2]\) \(449280\) \(2.0517\)  
39326.m3 39326l4 \([1, 1, 1, -99778, -9985145]\) \(4956477625/941192\) \(20860919379725768\) \([2]\) \(299520\) \(1.8489\)  
39326.m4 39326l2 \([1, 1, 1, -29553, 1941869]\) \(128787625/98\) \(2172107390642\) \([2]\) \(99840\) \(1.2996\)  
39326.m5 39326l1 \([1, 1, 1, -1463, 42985]\) \(-15625/28\) \(-620602111612\) \([2]\) \(49920\) \(0.95306\) \(\Gamma_0(N)\)-optimal
39326.m6 39326l3 \([1, 1, 1, 12582, -906457]\) \(9938375/21952\) \(-486552055503808\) \([2]\) \(149760\) \(1.5024\)