Properties

Label 76050p
Number of curves $1$
Conductor $76050$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 76050p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76050.a1 76050p1 \([1, -1, 0, -4720031367, 147697594324541]\) \(-74168622330075/17179869184\) \(-2693754461912700026880000000000\) \([]\) \(210038400\) \(4.5585\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 76050p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 76050p do not have complex multiplication.

Modular form 76050.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 5 q^{7} - q^{8} - 2 q^{11} + 5 q^{14} + q^{16} - 2 q^{17} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display