Properties

Label 31478a
Number of curves $1$
Conductor $31478$
CM no
Rank $1$

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

Elliptic curves in class 31478a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31478.b1 31478a1 \([1, 1, 0, -151, -781]\) \(-384716455417/31478\) \(-31478\) \([]\) \(5116\) \(-0.092111\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 31478a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 31478a do not have complex multiplication.

Modular form 31478.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 2 q^{5} + q^{6} - q^{7} - q^{8} - 2 q^{9} + 2 q^{10} + 4 q^{11} - q^{12} - 6 q^{13} + q^{14} + 2 q^{15} + q^{16} + 4 q^{17} + 2 q^{18} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display