Properties

Label 51714.d
Number of curves $1$
Conductor $51714$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 51714.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51714.d1 51714e1 \([1, -1, 0, -2417661, 1447796533]\) \(-2628062448817/594864\) \(-353746404080752176\) \([]\) \(1397760\) \(2.3595\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 51714.d1 has rank \(0\).

Complex multiplication

The elliptic curves in class 51714.d do not have complex multiplication.

Modular form 51714.2.a.d

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