Properties

Label 42135.d
Number of curves $1$
Conductor $42135$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 42135.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42135.d1 42135a1 \([0, -1, 1, -99251, -11729578]\) \(1736704/45\) \(2801686068511245\) \([]\) \(183168\) \(1.7460\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 42135.d1 has rank \(0\).

Complex multiplication

The elliptic curves in class 42135.d do not have complex multiplication.

Modular form 42135.2.a.d

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