Properties

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

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 247962.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
247962.s1 247962s1 \([1, 0, 1, -14890, 2211548]\) \(-15124197817/78881088\) \(-1903997704395072\) \([]\) \(1410048\) \(1.6161\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 247962.s1 has rank \(1\).

Complex multiplication

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

Modular form 247962.2.a.s

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