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Properties

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

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Show commands: SageMath
Copy content sage:E = EllipticCurve("tt1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

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

Complex multiplication

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

Modular form 435600.2.a.tt

Copy content sage:E.q_eigenform(10)
 
\(q + 4 q^{7} + 5 q^{13} - 7 q^{19} + O(q^{20})\) 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.tt

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435600.tt1 435600tt2 \([0, 0, 0, -401115, 113228170]\) \(-53969305/10648\) \(-1408158815632588800\) \([]\) \(7464960\) \(2.2055\) \(\Gamma_0(N)\)-optimal*
435600.tt2 435600tt1 \([0, 0, 0, 34485, -811910]\) \(34295/22\) \(-2909419040563200\) \([]\) \(2488320\) \(1.6562\) \(\Gamma_0(N)\)-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.tt1.