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Properties

Label 458640in
Number of curves $2$
Conductor $458640$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("in1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 458640in have rank \(0\).

Complex multiplication

The elliptic curves in class 458640in do not have complex multiplication.

Modular form 458640.2.a.in

Copy content sage:E.q_eigenform(10)
 
\(q + q^{5} - 4 q^{11} + q^{13} + 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.

Elliptic curves in class 458640in

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
458640.in2 458640in1 \([0, 0, 0, -34680387, -76242232766]\) \(38282975119927/1314144000\) \(158348076757772009472000\) \([2]\) \(41287680\) \(3.2234\) \(\Gamma_0(N)\)-optimal*
458640.in1 458640in2 \([0, 0, 0, -86048067, 202139772226]\) \(584759426925367/191909250000\) \(23124148228448676864000000\) \([2]\) \(82575360\) \(3.5699\) \(\Gamma_0(N)\)-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 458640in1.