Properties

Label 55860l
Number of curves $4$
Conductor $55860$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("l1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 55860l have rank \(0\).

L-function data

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

Complex multiplication

The elliptic curves in class 55860l do not have complex multiplication.

Modular form 55860.2.a.l

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} + 4 q^{13} - q^{15} - 6 q^{17} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 55860l

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55860.k4 55860l1 \([0, -1, 0, -59845, -5614538]\) \(12592337649664/1315845\) \(2476925574480\) \([2]\) \(207360\) \(1.4101\) \(\Gamma_0(N)\)-optimal
55860.k3 55860l2 \([0, -1, 0, -64500, -4685400]\) \(985329269584/252434475\) \(7602857868614400\) \([2]\) \(414720\) \(1.7567\)  
55860.k2 55860l3 \([0, -1, 0, -130405, 9938650]\) \(130287139815424/52926616125\) \(99628215367842000\) \([2]\) \(622080\) \(1.9594\)  
55860.k1 55860l4 \([0, -1, 0, -1810860, 938221992]\) \(21804712949838544/8680921875\) \(261453255084000000\) \([2]\) \(1244160\) \(2.3060\)