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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 7744.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7744.m1 | 7744h2 | \([0, -1, 0, -37429, 2815661]\) | \(-199794688/1331\) | \(-38632614969344\) | \([]\) | \(23040\) | \(1.4425\) | |
| 7744.m2 | 7744h1 | \([0, -1, 0, 1291, 20077]\) | \(8192/11\) | \(-319277809664\) | \([]\) | \(7680\) | \(0.89323\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7744.m have rank \(0\).
Complex multiplication
The elliptic curves in class 7744.m do not have complex multiplication.Modular form 7744.2.a.m
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
