Properties

Label 213444.o
Number of curves $1$
Conductor $213444$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 213444.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
213444.o1 213444j1 \([0, 0, 0, 1342438251, 9458447498269]\) \(110056273881297152/79587574568271\) \(-193480469147435685662310572016\) \([]\) \(193536000\) \(4.3079\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 213444.o1 has rank \(1\).

Complex multiplication

The elliptic curves in class 213444.o do not have complex multiplication.

Modular form 213444.2.a.o

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