Properties

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

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 316239t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
316239.t1 316239t1 \([0, 1, 1, -43738280024, -3520808978639917]\) \(-3606604082099922073056514048/162252863054667\) \(-416296455675219532600803\) \([]\) \(820931328\) \(4.4616\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 316239t1 has rank \(1\).

Complex multiplication

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

Modular form 316239.2.a.t

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