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Properties

Label 421652.c
Number of curves $1$
Conductor $421652$
CM no
Rank $1$

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

Rank

Copy content sage:E.rank()
 

The elliptic curve 421652.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 421652.c do not have complex multiplication.

Modular form 421652.2.a.c

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - q^{7} - 2 q^{9} + q^{11} + 4 q^{13} - q^{15} + 6 q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 421652.c

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
421652.c1 421652c1 \([0, -1, 0, -29205, 2133409]\) \(-4194304/539\) \(-354029192819456\) \([]\) \(1177632\) \(1.5253\) \(\Gamma_0(N)\)-optimal