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Properties

Label 435600.ma
Number of curves $2$
Conductor $435600$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ma1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 435600.ma have rank \(0\).

Complex multiplication

The elliptic curves in class 435600.ma do not have complex multiplication.

Modular form 435600.2.a.ma

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 435600.ma

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435600.ma1 435600ma1 \([0, 0, 0, -264636075, -1683828467750]\) \(-1693700041/32000\) \(-38724367429896192000000000\) \([]\) \(109486080\) \(3.7045\) \(\Gamma_0(N)\)-optimal*
435600.ma2 435600ma2 \([0, 0, 0, 1053053925, -7873018397750]\) \(106718863559/83886080\) \(-101513605755427073556480000000\) \([]\) \(328458240\) \(4.2538\) \(\Gamma_0(N)\)-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 435600.ma1.