Properties

Label 21780.a
Number of curves $1$
Conductor $21780$
CM no
Rank $2$

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

Elliptic curves in class 21780.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21780.a1 21780m1 \([0, 0, 0, -5808, 182468]\) \(-7929856/675\) \(-1844344339200\) \([]\) \(34560\) \(1.0984\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 21780.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 21780.a do not have complex multiplication.

Modular form 21780.2.a.a

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