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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 1638.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1638.m1 | 1638l1 | \([1, -1, 1, -3749, 89437]\) | \(-215773279370739/447469568\) | \(-12081678336\) | \([]\) | \(1760\) | \(0.82044\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1638.m1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1638.m do not have complex multiplication.Modular form 1638.2.a.m
sage: E.q_eigenform(10)