Properties

Label 490245bc
Number of curves $1$
Conductor $490245$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 490245bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
490245.bc1 490245bc1 \([0, -1, 1, -519287855, 4554880579178]\) \(-131631542171643599790505984/44988384234391875\) \(-5292838416791969701875\) \([]\) \(125798400\) \(3.5250\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 490245bc1 has rank \(2\).

Complex multiplication

The elliptic curves in class 490245bc do not have complex multiplication.

Modular form 490245.2.a.bc

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{4} + q^{5} + q^{9} - 4 q^{11} + 2 q^{12} + 5 q^{13} - q^{15} + 4 q^{16} - 7 q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display