Properties

Label 42526.a
Number of curves $1$
Conductor $42526$
CM no
Rank $3$

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

Elliptic curves in class 42526.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42526.a1 42526b1 \([1, 0, 1, -78, 272]\) \(-51520374361/3742288\) \(-3742288\) \([]\) \(21120\) \(0.010740\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 42526.a1 has rank \(3\).

Complex multiplication

The elliptic curves in class 42526.a do not have complex multiplication.

Modular form 42526.2.a.a

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