Properties

Label 312050n
Number of curves $1$
Conductor $312050$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 312050n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
312050.n1 312050n1 \([1, 1, 1, -549338, -147812469]\) \(4826809/316\) \(1200244311634937500\) \([]\) \(6988800\) \(2.2189\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 312050n1 has rank \(1\).

Complex multiplication

The elliptic curves in class 312050n do not have complex multiplication.

Modular form 312050.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} - 3 q^{7} + q^{8} - 2 q^{9} + 4 q^{11} - q^{12} + 7 q^{13} - 3 q^{14} + q^{16} - 4 q^{17} - 2 q^{18} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display