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Properties

Label 413712.bk
Number of curves $2$
Conductor $413712$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bk1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 413712.bk have rank \(0\).

Complex multiplication

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

Modular form 413712.2.a.bk

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

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.

Elliptic curves in class 413712.bk

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
413712.bk1 413712bk1 \([0, 0, 0, -1535196, 525186259]\) \(7107347955712/1996623837\) \(112409722712122095312\) \([2]\) \(9289728\) \(2.5544\) \(\Gamma_0(N)\)-optimal
413712.bk2 413712bk2 \([0, 0, 0, 4008849, 3451333210]\) \(7909612346288/10289870721\) \(-9269099110659922350336\) \([2]\) \(18579456\) \(2.9010\)