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Properties

Label 436800.mv
Number of curves $4$
Conductor $436800$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("mv1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 436800.mv have rank \(1\).

Complex multiplication

The elliptic curves in class 436800.mv do not have complex multiplication.

Modular form 436800.2.a.mv

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} - q^{7} + q^{9} + q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 436800.mv

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
436800.mv1 436800mv3 \([0, 1, 0, -901633, 329184863]\) \(19790357598649/2998905\) \(12283514880000000\) \([2]\) \(4718592\) \(2.0999\) \(\Gamma_0(N)\)-optimal*
436800.mv2 436800mv4 \([0, 1, 0, -373633, -84815137]\) \(1408317602329/58524375\) \(239715840000000000\) \([2]\) \(4718592\) \(2.0999\)  
436800.mv3 436800mv2 \([0, 1, 0, -61633, 4104863]\) \(6321363049/1863225\) \(7631769600000000\) \([2, 2]\) \(2359296\) \(1.7534\) \(\Gamma_0(N)\)-optimal*
436800.mv4 436800mv1 \([0, 1, 0, 10367, 432863]\) \(30080231/36855\) \(-150958080000000\) \([2]\) \(1179648\) \(1.4068\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 436800.mv1.