Properties

Label 425880.cn
Number of curves $4$
Conductor $425880$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cn1")
 
E.isogeny_class()
 

Elliptic curves in class 425880.cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
425880.cn1 425880cn3 \([0, 0, 0, -37989003, 90122728358]\) \(841356017734178/1404585\) \(10121983396954490880\) \([2]\) \(27525120\) \(2.9090\) \(\Gamma_0(N)\)-optimal*
425880.cn2 425880cn4 \([0, 0, 0, -6230523, -4131840778]\) \(3711757787138/1124589375\) \(8104226502590749440000\) \([2]\) \(27525120\) \(2.9090\)  
425880.cn3 425880cn2 \([0, 0, 0, -2397603, 1379131598]\) \(423026849956/16769025\) \(60422043747126297600\) \([2, 2]\) \(13762560\) \(2.5624\) \(\Gamma_0(N)\)-optimal*
425880.cn4 425880cn1 \([0, 0, 0, 66417, 78621842]\) \(35969456/2985255\) \(-2689112935998478080\) \([2]\) \(6881280\) \(2.2158\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 425880.cn1.

Rank

sage: E.rank()
 

The elliptic curves in class 425880.cn have rank \(0\).

Complex multiplication

The elliptic curves in class 425880.cn do not have complex multiplication.

Modular form 425880.2.a.cn

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} + 4 q^{11} - 6 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.