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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 3744.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3744.a1 | 3744d1 | \([0, 0, 0, -26121, -1624444]\) | \(42246001231552/14414517\) | \(672523705152\) | \([2]\) | \(6144\) | \(1.2411\) | \(\Gamma_0(N)\)-optimal |
| 3744.a2 | 3744d2 | \([0, 0, 0, -22476, -2093920]\) | \(-420526439488/390971529\) | \(-1167434730049536\) | \([2]\) | \(12288\) | \(1.5877\) |
Rank
sage: E.rank()
The elliptic curves in class 3744.a have rank \(0\).
Complex multiplication
The elliptic curves in class 3744.a do not have complex multiplication.Modular form 3744.2.a.a
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.
