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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 12075.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12075.m1 | 12075h1 | \([0, -1, 1, 729217, -539549032]\) | \(2744564518708084736/9629735831296875\) | \(-150464622364013671875\) | \([]\) | \(224640\) | \(2.5547\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12075.m1 has rank \(0\).
Complex multiplication
The elliptic curves in class 12075.m do not have complex multiplication.Modular form 12075.2.a.m
sage: E.q_eigenform(10)