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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 177744.cm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177744.cm1 | 177744l1 | \([0, 1, 0, -5205536, -4588646412]\) | \(-25727239787761/101406816\) | \(-61488530051970760704\) | \([]\) | \(4561920\) | \(2.6547\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 177744.cm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 177744.cm do not have complex multiplication.Modular form 177744.2.a.cm
sage: E.q_eigenform(10)