Properties

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

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 3042.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3042.m1 3042j1 \([1, -1, 1, -32, 2643]\) \(-169/144\) \(-2998219536\) \([]\) \(1536\) \(0.49748\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3042.m1 has rank \(1\).

Complex multiplication

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

Modular form 3042.2.a.m

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