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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 1344.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1344.h1 | 1344k3 | \([0, -1, 0, -897, -10047]\) | \(2438569736/21\) | \(688128\) | \([2]\) | \(512\) | \(0.28794\) | |
| 1344.h2 | 1344k2 | \([0, -1, 0, -57, -135]\) | \(5088448/441\) | \(1806336\) | \([2, 2]\) | \(256\) | \(-0.058633\) | |
| 1344.h3 | 1344k1 | \([0, -1, 0, -12, 18]\) | \(3241792/567\) | \(36288\) | \([2]\) | \(128\) | \(-0.40521\) | \(\Gamma_0(N)\)-optimal |
| 1344.h4 | 1344k4 | \([0, -1, 0, 63, -735]\) | \(830584/7203\) | \(-236027904\) | \([2]\) | \(512\) | \(0.28794\) |
Rank
sage: E.rank()
The elliptic curves in class 1344.h have rank \(0\).
Complex multiplication
The elliptic curves in class 1344.h do not have complex multiplication.Modular form 1344.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
