Properties

Label 502507.a
Number of curves $1$
Conductor $502507$
CM no
Rank $1$

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

Elliptic curves in class 502507.a

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
502507.a1 \([0, -1, 1, -58, 194]\) \(-21952000000/502507\) \(-502507\) \([]\) \(175664\) \(-0.11844\)

Rank

sage: E.rank()
 

The elliptic curve 502507.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 502507.a do not have complex multiplication.

Modular form 502507.2.a.a

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