Properties

Label 47096.a
Number of curves $1$
Conductor $47096$
CM no
Rank $1$

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

Elliptic curves in class 47096.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47096.a1 47096g1 \([0, 0, 0, 29, -1682]\) \(108/49\) \(-1223742464\) \([]\) \(41216\) \(0.42285\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 47096.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 47096.a do not have complex multiplication.

Modular form 47096.2.a.a

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