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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 64974h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64974.d2 | 64974h1 | \([1, 1, 0, 29984, 10690240]\) | \(8691118430696801/148627738838592\) | \(-50979314421637056\) | \([2]\) | \(666624\) | \(1.8864\) | \(\Gamma_0(N)\)-optimal |
| 64974.d1 | 64974h2 | \([1, 1, 0, -582376, 160963384]\) | \(63685588278222463519/4124615136744024\) | \(1414742991903200232\) | \([2]\) | \(1333248\) | \(2.2329\) |
Rank
sage: E.rank()
The elliptic curves in class 64974h have rank \(1\).
Complex multiplication
The elliptic curves in class 64974h do not have complex multiplication.Modular form 64974.2.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.
