Properties

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

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Show commands: SageMath
E = EllipticCurve("ca1")
 
E.isogeny_class()
 

Elliptic curves in class 162624.ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162624.ca1 162624hq1 \([0, -1, 0, -1701, 19197]\) \(274717696/83349\) \(165236391936\) \([]\) \(184320\) \(0.85758\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 162624.ca1 has rank \(1\).

Complex multiplication

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

Modular form 162624.2.a.ca

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} + 6 q^{13} + q^{15} + 3 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display