Properties

Label 1035.b
Number of curves $1$
Conductor $1035$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 1035.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1035.b1 1035e1 \([0, 0, 1, 63, 290]\) \(37933056/71875\) \(-52396875\) \([]\) \(320\) \(0.16582\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1035.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1035.b do not have complex multiplication.

Modular form 1035.2.a.b

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