Properties

Label 21294r
Number of curves $1$
Conductor $21294$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 21294r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21294.g1 21294r1 \([1, -1, 0, -1804698, -1296161996]\) \(-6468095257/3483648\) \(-350102584911920375808\) \([]\) \(823680\) \(2.6459\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 21294r1 has rank \(0\).

Complex multiplication

The elliptic curves in class 21294r do not have complex multiplication.

Modular form 21294.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 2 q^{5} - q^{7} - q^{8} + 2 q^{10} + q^{14} + q^{16} - q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display