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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 74529.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 74529.h1 | 74529bm2 | \([1, -1, 1, -236606, 43108706]\) | \(22665187/729\) | \(47115898083138339\) | \([2]\) | \(645120\) | \(1.9734\) | |
| 74529.h2 | 74529bm1 | \([1, -1, 1, -35951, -1677490]\) | \(79507/27\) | \(1745033262338457\) | \([2]\) | \(322560\) | \(1.6268\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 74529.h have rank \(0\).
Complex multiplication
The elliptic curves in class 74529.h do not have complex multiplication.Modular form 74529.2.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.
