Properties

Label 322624a
Number of curves $1$
Conductor $322624$
CM no
Rank $2$

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

Elliptic curves in class 322624a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
322624.a1 322624a1 \([0, 0, 0, -847271116, -9453425934224]\) \(2003092024307193/9529458688\) \(320006091845465579362189312\) \([]\) \(313528320\) \(3.9351\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 322624a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 322624a do not have complex multiplication.

Modular form 322624.2.a.a

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} - 2 q^{5} + 3 q^{7} + 6 q^{9} - 6 q^{11} - 5 q^{13} + 6 q^{15} - 6 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display