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Properties

Label 413712.i
Number of curves $1$
Conductor $413712$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("i1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 413712.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 413712.i do not have complex multiplication.

Modular form 413712.2.a.i

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

Elliptic curves in class 413712.i

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
413712.i1 413712i1 \([0, 0, 0, -8112, -500240]\) \(-692224/867\) \(-73940091383808\) \([]\) \(1674240\) \(1.3546\) \(\Gamma_0(N)\)-optimal