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Properties

Label 412984m
Number of curves $1$
Conductor $412984$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("m1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 412984m1 has rank \(1\).

Complex multiplication

The elliptic curves in class 412984m do not have complex multiplication.

Modular form 412984.2.a.m

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

Elliptic curves in class 412984m

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
412984.m1 412984m1 \([0, 1, 0, -814536, 308576048]\) \(-620302509218/68710213\) \(-6620226568770873344\) \([]\) \(5713920\) \(2.3489\) \(\Gamma_0(N)\)-optimal