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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 11712.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11712.h1 | 11712b2 | \([0, -1, 0, -32961, -2883903]\) | \(-15107691357361/5067577806\) | \(-1328435116376064\) | \([]\) | \(57600\) | \(1.6139\) | |
| 11712.h2 | 11712b1 | \([0, -1, 0, -321, 17217]\) | \(-13997521/474336\) | \(-124344336384\) | \([]\) | \(11520\) | \(0.80916\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11712.h have rank \(1\).
Complex multiplication
The elliptic curves in class 11712.h do not have complex multiplication.Modular form 11712.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
