Properties

Label 42093.a
Number of curves $1$
Conductor $42093$
CM no
Rank $3$

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

Elliptic curves in class 42093.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42093.a1 42093a1 \([0, 0, 1, -21, 22]\) \(4214784/1559\) \(378837\) \([]\) \(13248\) \(-0.22955\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 42093.a1 has rank \(3\).

Complex multiplication

The elliptic curves in class 42093.a do not have complex multiplication.

Modular form 42093.2.a.a

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