Properties

Label 126350.a
Number of curves $1$
Conductor $126350$
CM no
Rank $1$

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

Elliptic curves in class 126350.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
126350.a1 126350j1 \([1, -1, 0, -40157569492, -3097403860376084]\) \(2272707362766267675/67228\) \(211852036584830195312500\) \([]\) \(314640000\) \(4.4334\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 126350.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 126350.a do not have complex multiplication.

Modular form 126350.2.a.a

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