Properties

Label 457776.r
Number of curves $1$
Conductor $457776$
CM no
Rank $0$

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

Elliptic curves in class 457776.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
457776.r1 457776r1 \([0, 0, 0, 58956, -16370116]\) \(17408/99\) \(-128882531910249216\) \([]\) \(3760128\) \(1.9651\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 457776.r1 has rank \(0\).

Complex multiplication

The elliptic curves in class 457776.r do not have complex multiplication.

Modular form 457776.2.a.r

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