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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 1456h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1456.k2 | 1456h1 | \([0, -1, 0, -117, -451]\) | \(-43614208/91\) | \(-372736\) | \([]\) | \(288\) | \(-0.045361\) | \(\Gamma_0(N)\)-optimal |
| 1456.k3 | 1456h2 | \([0, -1, 0, 203, -2499]\) | \(224755712/753571\) | \(-3086626816\) | \([]\) | \(864\) | \(0.50395\) | |
| 1456.k1 | 1456h3 | \([0, -1, 0, -1877, 77789]\) | \(-178643795968/524596891\) | \(-2148748865536\) | \([]\) | \(2592\) | \(1.0533\) |
Rank
sage: E.rank()
The elliptic curves in class 1456h have rank \(1\).
Complex multiplication
The elliptic curves in class 1456h do not have complex multiplication.Modular form 1456.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
