Properties

Label 140679bc
Number of curves $1$
Conductor $140679$
CM no
Rank $1$

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

Elliptic curves in class 140679bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
140679.bb1 140679bc1 \([1, -1, 0, -115845, 26928404]\) \(-74246873427/92019697\) \(-213088656616704099\) \([]\) \(1078272\) \(2.0185\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 140679bc1 has rank \(1\).

Complex multiplication

The elliptic curves in class 140679bc do not have complex multiplication.

Modular form 140679.2.a.bc

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - q^{5} - 3 q^{8} - q^{10} + q^{11} - q^{13} - q^{16} - 7 q^{17} + O(q^{20})\) Copy content Toggle raw display