Properties

Label 493680.r
Number of curves $1$
Conductor $493680$
CM no
Rank $0$

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

Elliptic curves in class 493680.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
493680.r1 493680r1 \([0, -1, 0, 254544, 151654131]\) \(64347918907136/388153407375\) \(-11002199016362598000\) \([]\) \(7996800\) \(2.3356\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 493680.r1 has rank \(0\).

Complex multiplication

The elliptic curves in class 493680.r do not have complex multiplication.

Modular form 493680.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} - 4 q^{13} + q^{15} - q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display