Properties

Label 123627.a
Number of curves $1$
Conductor $123627$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 123627.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
123627.a1 123627m1 \([0, -1, 1, -673080, 2979633152]\) \(-200704/22707\) \(-3815295211687913161803\) \([]\) \(14817600\) \(2.8206\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 123627.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 123627.a do not have complex multiplication.

Modular form 123627.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} + q^{9} + 8 q^{10} - 4 q^{11} - 2 q^{12} - q^{13} + 4 q^{15} - 4 q^{16} + 2 q^{17} - 2 q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display