Properties

Label 42483a
Number of curves $1$
Conductor $42483$
CM no
Rank $1$

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

Elliptic curves in class 42483a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42483.t1 42483a1 \([1, 1, 0, -64019, -4764234]\) \(208537/51\) \(7096562377347219\) \([]\) \(338688\) \(1.7522\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 42483a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 42483a do not have complex multiplication.

Modular form 42483.2.a.a

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