Properties

Label 3042.d
Number of curves $1$
Conductor $3042$
CM no
Rank $0$

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

Elliptic curves in class 3042.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3042.d1 3042c1 \([1, -1, 0, -5355, 5791189]\) \(-169/144\) \(-14471833040340624\) \([]\) \(19968\) \(1.7799\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3042.d1 has rank \(0\).

Complex multiplication

The elliptic curves in class 3042.d do not have complex multiplication.

Modular form 3042.2.a.d

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