Properties

Label 414736.ch
Number of curves $1$
Conductor $414736$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ch1")
 
E.isogeny_class()
 

Elliptic curves in class 414736.ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
414736.ch1 414736ch1 \([0, 0, 0, -218228899, -1258941159427]\) \(-4124632486295808/70140333767\) \(-19545332683641447742689392\) \([]\) \(136249344\) \(3.6514\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 414736.ch1 has rank \(1\).

Complex multiplication

The elliptic curves in class 414736.ch do not have complex multiplication.

Modular form 414736.2.a.ch

sage: E.q_eigenform(10)
 
\(q + 3 q^{3} + 2 q^{5} + 6 q^{9} + 2 q^{11} + q^{13} + 6 q^{15} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display