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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 9744.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9744.m1 | 9744r1 | \([0, 1, 0, 2691856, 3086110932]\) | \(526646344431378309263/1308681048044740608\) | \(-5360357572791257530368\) | \([]\) | \(471744\) | \(2.8533\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 9744.m1 has rank \(0\).
Complex multiplication
The elliptic curves in class 9744.m do not have complex multiplication.Modular form 9744.2.a.m
sage: E.q_eigenform(10)