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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 14504h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14504.f1 | 14504h1 | \([0, 0, 0, -827218, 289586325]\) | \(33256413948450816/2481997\) | \(4672071440848\) | \([2]\) | \(117504\) | \(1.8807\) | \(\Gamma_0(N)\)-optimal |
14504.f2 | 14504h2 | \([0, 0, 0, -825503, 290846850]\) | \(-2065624967846736/17960084863\) | \(-540924422156054272\) | \([2]\) | \(235008\) | \(2.2273\) |
Rank
sage: E.rank()
The elliptic curves in class 14504h have rank \(1\).
Complex multiplication
The elliptic curves in class 14504h do not have complex multiplication.Modular form 14504.2.a.h
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.