Properties

Label 10304.a
Number of curves $1$
Conductor $10304$
CM no
Rank $1$

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

Elliptic curves in class 10304.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10304.a1 10304b1 \([0, 0, 0, -33676, 2413336]\) \(-4124632486295808/70140333767\) \(-71823701777408\) \([]\) \(43008\) \(1.4573\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10304.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 10304.a do not have complex multiplication.

Modular form 10304.2.a.a

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