Properties

Label 247962.z
Number of curves $1$
Conductor $247962$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 247962.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
247962.z1 247962z1 \([1, 1, 1, -1205425, 438506639]\) \(27768533625361/4134297024\) \(28839853228472155584\) \([]\) \(7931520\) \(2.4585\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 247962.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 247962.z do not have complex multiplication.

Modular form 247962.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + 3 q^{7} + q^{8} + q^{9} + q^{10} + q^{11} - q^{12} + q^{13} + 3 q^{14} - q^{15} + q^{16} + q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display