Properties

Label 1325.a
Number of curves $1$
Conductor $1325$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 1325.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1325.a1 1325e1 \([0, 1, 1, -8, -6]\) \(102400/53\) \(33125\) \([]\) \(216\) \(-0.44065\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1325.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 1325.a do not have complex multiplication.

Modular form 1325.2.a.a

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