Properties

Label 251896f
Number of curves $1$
Conductor $251896$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 251896f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
251896.f1 251896f1 \([0, -1, 0, -5932, 183953]\) \(-562432/23\) \(-944187318512\) \([]\) \(414720\) \(1.0653\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 251896f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 251896f do not have complex multiplication.

Modular form 251896.2.a.f

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