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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 63210h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 63210.k3 | 63210h1 | \([1, 1, 0, -3357, 73389]\) | \(35578826569/51600\) | \(6070688400\) | \([2]\) | \(55296\) | \(0.77930\) | \(\Gamma_0(N)\)-optimal |
| 63210.k2 | 63210h2 | \([1, 1, 0, -4337, 25761]\) | \(76711450249/41602500\) | \(4894492522500\) | \([2, 2]\) | \(110592\) | \(1.1259\) | |
| 63210.k4 | 63210h3 | \([1, 1, 0, 16733, 223819]\) | \(4403686064471/2721093750\) | \(-320133958593750\) | \([2]\) | \(221184\) | \(1.4724\) | |
| 63210.k1 | 63210h4 | \([1, 1, 0, -41087, -3200889]\) | \(65202655558249/512820150\) | \(60332777827350\) | \([2]\) | \(221184\) | \(1.4724\) |
Rank
sage: E.rank()
The elliptic curves in class 63210h have rank \(1\).
Complex multiplication
The elliptic curves in class 63210h do not have complex multiplication.Modular form 63210.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
