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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 21675m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
21675.r1 | 21675m1 | \([1, 1, 0, -21825, 222750]\) | \(35242105/19683\) | \(642165563671875\) | \([]\) | \(68040\) | \(1.5316\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 21675m1 has rank \(1\).
Complex multiplication
The elliptic curves in class 21675m do not have complex multiplication.Modular form 21675.2.a.m
sage: E.q_eigenform(10)