Properties

Label 31478.a
Number of curves $1$
Conductor $31478$
CM no
Rank $3$

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

Elliptic curves in class 31478.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31478.a1 31478b1 \([1, 0, 1, -5, 12]\) \(-10218313/62956\) \(-62956\) \([]\) \(5536\) \(-0.39551\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 31478.a1 has rank \(3\).

Complex multiplication

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

Modular form 31478.2.a.a

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