Properties

Label 252700c
Number of curves $1$
Conductor $252700$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 252700c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
252700.c1 252700c1 \([0, 0, 0, -361000, -85737500]\) \(-221184/7\) \(-164660583500000000\) \([]\) \(4354560\) \(2.0798\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 252700c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 252700c do not have complex multiplication.

Modular form 252700.2.a.c

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} + q^{7} + 6 q^{9} + 3 q^{11} - q^{13} - 5 q^{17} + O(q^{20})\) Copy content Toggle raw display