Properties

Label 75690j
Number of curves $1$
Conductor $75690$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 75690j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75690.j1 75690j1 \([1, -1, 0, -1361038815, -14503447037619]\) \(764581408291686481/193273528320000\) \(70482919772286865196974080000\) \([]\) \(77952000\) \(4.2452\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75690j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 75690j do not have complex multiplication.

Modular form 75690.2.a.j

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