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Properties

Label 421800.a
Number of curves $1$
Conductor $421800$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("a1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 421800.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 421800.a do not have complex multiplication.

Modular form 421800.2.a.a

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

Elliptic curves in class 421800.a

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
421800.a1 421800a1 \([0, -1, 0, -18210371433, -945855687809763]\) \(-166962959078001445737309395968/599433319281236638491\) \(-2397733277124946553964000000\) \([]\) \(1113937920\) \(4.4714\) \(\Gamma_0(N)\)-optimal