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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 37180.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37180.h1 | 37180f1 | \([0, -1, 0, -40785, -2786278]\) | \(97152876544/12371645\) | \(955449078892880\) | \([2]\) | \(177408\) | \(1.6035\) | \(\Gamma_0(N)\)-optimal |
| 37180.h2 | 37180f2 | \([0, -1, 0, 61460, -14605800]\) | \(20777545136/86397025\) | \(-106757616087865600\) | \([2]\) | \(354816\) | \(1.9500\) |
Rank
sage: E.rank()
The elliptic curves in class 37180.h have rank \(1\).
Complex multiplication
The elliptic curves in class 37180.h do not have complex multiplication.Modular form 37180.2.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.
