Properties

Label 254512c
Number of curves $1$
Conductor $254512$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 254512c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
254512.c1 254512c1 \([0, -1, 0, 40, -784]\) \(1685159/63628\) \(-260620288\) \([]\) \(139392\) \(0.29477\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 254512c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 254512c do not have complex multiplication.

Modular form 254512.2.a.c

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - 4 q^{5} + 4 q^{7} + q^{9} + 2 q^{11} - 4 q^{13} - 8 q^{15} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display