Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 67270o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67270.c1 | 67270o1 | \([1, -1, 0, -119344, -15728672]\) | \(211815318681/1701280\) | \(1509892262411680\) | \([]\) | \(691200\) | \(1.7399\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 67270o1 has rank \(1\).
Complex multiplication
The elliptic curves in class 67270o do not have complex multiplication.Modular form 67270.2.a.o
sage: E.q_eigenform(10)