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Properties

Label 462722.d
Number of curves $1$
Conductor $462722$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("d1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 462722.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 462722.d do not have complex multiplication.

Modular form 462722.2.a.d

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

Elliptic curves in class 462722.d

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462722.d1 462722d1 \([1, -1, 0, -89348726, -1119560271244]\) \(-4652805537/29246464\) \(-495846523052183705180087296\) \([]\) \(143216640\) \(3.8059\) \(\Gamma_0(N)\)-optimal