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Properties

Label 506251.a
Number of curves $1$
Conductor $506251$
CM no
Rank $2$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("a1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 506251.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 506251.a do not have complex multiplication.

Modular form 506251.2.a.a

Copy content sage:E.q_eigenform(10)
 
\(q - 2 q^{4} + q^{5} - 4 q^{7} - 3 q^{9} - 6 q^{11} - 6 q^{13} + 4 q^{16} - 6 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 506251.a

Copy content sage:E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
506251.a1 \([0, 0, 1, -2, 34]\) \(-884736/506251\) \(-506251\) \([]\) \(69600\) \(-0.22635\)