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SageMath
E = EllipticCurve("dp1")
E.isogeny_class()
Elliptic curves in class 106722dp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106722.dq1 | 106722dp1 | \([1, -1, 0, -5302908, -4871375888]\) | \(-260607143968297/11270993184\) | \(-713250207121712841504\) | \([]\) | \(8064000\) | \(2.7671\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 106722dp1 has rank \(0\).
Complex multiplication
The elliptic curves in class 106722dp do not have complex multiplication.Modular form 106722.2.a.dp
sage: E.q_eigenform(10)