Properties

Label 162624.i
Number of curves $1$
Conductor $162624$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 162624.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162624.i1 162624cf1 \([0, -1, 0, 7583, -608639]\) \(50250332/194481\) \(-186606965293056\) \([]\) \(491520\) \(1.4211\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 162624.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 162624.i do not have complex multiplication.

Modular form 162624.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{5} - q^{7} + q^{9} + q^{13} + 3 q^{15} - 5 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display