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Properties

Label 400710.o
Number of curves $1$
Conductor $400710$
CM no
Rank $1$

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

Rank

Copy content sage:E.rank()
 

The elliptic curve 400710.o1 has rank \(1\).

Complex multiplication

The elliptic curves in class 400710.o do not have complex multiplication.

Modular form 400710.2.a.o

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - 2 q^{7} - q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} - 6 q^{13} + 2 q^{14} - q^{15} + q^{16} + 7 q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 400710.o

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
400710.o1 400710o1 \([1, 0, 1, -11199, 80372122]\) \(-3301293169/59315625000\) \(-2790555835190625000\) \([]\) \(9123840\) \(2.2183\) \(\Gamma_0(N)\)-optimal