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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 194208.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 194208.h1 | 194208bz2 | \([0, -1, 0, -1685544, -18539532]\) | \(42852953779784/24786408969\) | \(306321232256745656832\) | \([2]\) | \(6635520\) | \(2.6204\) | |
| 194208.h2 | 194208bz1 | \([0, -1, 0, 421266, -2527776]\) | \(5352028359488/3098832471\) | \(-4787090085644991936\) | \([2]\) | \(3317760\) | \(2.2738\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 194208.h have rank \(2\).
Complex multiplication
The elliptic curves in class 194208.h do not have complex multiplication.Modular form 194208.2.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 LMFDB 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 LMFDB labels.
