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Properties

Label 423360wb
Number of curves $2$
Conductor $423360$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve([0, 0, 0, -14112, -647584]) E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 423360wb have rank \(0\).

Complex multiplication

The elliptic curves in class 423360wb do not have complex multiplication.

Modular form 423360.2.a.wb

Copy content sage:E.q_eigenform(10)
 
\(q + q^{5} + 6 q^{11} - q^{13} + q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 423360wb

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
423360.wb1 423360wb1 \([0, 0, 0, -14112, -647584]\) \(-5971968/25\) \(-1301103820800\) \([]\) \(870912\) \(1.1795\) \(\Gamma_0(N)\)-optimal*
423360.wb2 423360wb2 \([0, 0, 0, 32928, -3413536]\) \(8429568/15625\) \(-7318708992000000\) \([]\) \(2612736\) \(1.7288\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 423360wb1.