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Properties

Label 473382w
Number of curves $1$
Conductor $473382$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("w1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 473382w1 has rank \(0\).

Complex multiplication

The elliptic curves in class 473382w do not have complex multiplication.

Modular form 473382.2.a.w

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} - q^{13} + q^{14} + q^{16} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 473382w

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
473382.w1 473382w1 \([1, -1, 0, -86511915, -311779687901]\) \(-4069400507818743889/31836860010774\) \(-560210551429727264767974\) \([]\) \(96215040\) \(3.3857\) \(\Gamma_0(N)\)-optimal