Show commands:
SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 121275dm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
121275.c1 | 121275dm1 | \([0, 0, 1, -1392825, 634753656]\) | \(-222985990144/841995\) | \(-1128353828928046875\) | \([]\) | \(3096576\) | \(2.3233\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 121275dm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 121275dm do not have complex multiplication.Modular form 121275.2.a.dm
sage: E.q_eigenform(10)