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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 32340.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32340.m1 | 32340g1 | \([0, -1, 0, -698805, -224472303]\) | \(61398847532302336/44027317125\) | \(27061654634784000\) | \([]\) | \(362880\) | \(2.0883\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 32340.m1 has rank \(1\).
Complex multiplication
The elliptic curves in class 32340.m do not have complex multiplication.Modular form 32340.2.a.m
sage: E.q_eigenform(10)