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SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 418950.eu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
418950.eu1 | 418950eu4 | \([1, -1, 0, -13598714817, -610366989022659]\) | \(207530301091125281552569/805586668007040\) | \(1079563181941853460810000000\) | \([2]\) | \(495452160\) | \(4.4004\) | |
418950.eu2 | 418950eu3 | \([1, -1, 0, -2577242817, 38883724417341]\) | \(1412712966892699019449/330160465517040000\) | \(442446600546105940653750000000\) | \([2]\) | \(495452160\) | \(4.4004\) | \(\Gamma_0(N)\)-optimal* |
418950.eu3 | 418950eu2 | \([1, -1, 0, -862634817, -9236749102659]\) | \(52974743974734147769/3152005008998400\) | \(4223988171786919737600000000\) | \([2, 2]\) | \(247726080\) | \(4.0538\) | \(\Gamma_0(N)\)-optimal* |
418950.eu4 | 418950eu1 | \([1, -1, 0, 40533183, -596140846659]\) | \(5495662324535111/117739817533440\) | \(-157782616204545884160000000\) | \([2]\) | \(123863040\) | \(3.7072\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 418950.eu have rank \(0\).
Complex multiplication
The elliptic curves in class 418950.eu do not have complex multiplication.Modular form 418950.2.a.eu
sage: E.q_eigenform(10)
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.