Properties

Label 804.a
Number of curves $1$
Conductor $804$
CM no
Rank $1$

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

Elliptic curves in class 804.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
804.a1 804c1 \([0, -1, 0, -12, 24]\) \(-810448/201\) \(-51456\) \([]\) \(72\) \(-0.37793\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 804.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 804.a do not have complex multiplication.

Modular form 804.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{5} + 3 q^{7} + q^{9} - 2 q^{11} + 2 q^{13} + 3 q^{15} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display