Properties

Label 50700p
Number of curves $1$
Conductor $50700$
CM no
Rank $1$

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

Elliptic curves in class 50700p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50700.c1 50700p1 \([0, -1, 0, -10243653, -12829937823]\) \(-769623354048512/15247889631\) \(-2355156828861359328000\) \([]\) \(2822400\) \(2.8938\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 50700p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 50700p do not have complex multiplication.

Modular form 50700.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{7} + q^{9} - 3 q^{11} + 3 q^{17} + O(q^{20})\) Copy content Toggle raw display