Properties

Label 25215.d
Number of curves $1$
Conductor $25215$
CM no
Rank $2$

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

Elliptic curves in class 25215.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25215.d1 25215f1 \([1, 0, 0, -691, 950]\) \(21708480289/12301875\) \(20679451875\) \([]\) \(18144\) \(0.66931\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 25215.d1 has rank \(2\).

Complex multiplication

The elliptic curves in class 25215.d do not have complex multiplication.

Modular form 25215.2.a.d

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