Properties

Label 316239p
Number of curves $1$
Conductor $316239$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 316239p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
316239.p1 316239p1 \([1, 0, 1, -1280044, 626568083]\) \(-66036512089/10085229\) \(-35424159650588232909\) \([]\) \(9270720\) \(2.4803\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 316239p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 316239p do not have complex multiplication.

Modular form 316239.2.a.p

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} - q^{5} + q^{6} + q^{7} - 3 q^{8} + q^{9} - q^{10} - q^{11} - q^{12} + 6 q^{13} + q^{14} - q^{15} - q^{16} - 2 q^{17} + q^{18} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display