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Properties

Label 453024dv
Number of curves $2$
Conductor $453024$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dv1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 453024dv have rank \(1\).

Complex multiplication

The elliptic curves in class 453024dv do not have complex multiplication.

Modular form 453024.2.a.dv

Copy content sage:E.q_eigenform(10)
 
\(q + 2 q^{5} + 4 q^{7} + q^{13} + 4 q^{17} - 6 q^{19} + O(q^{20})\) 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 453024dv

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
453024.dv2 453024dv1 \([0, 0, 0, -952149, -375634820]\) \(-1154981015488/69090879\) \(-5710634059427504064\) \([2]\) \(12165120\) \(2.3544\) \(\Gamma_0(N)\)-optimal*
453024.dv1 453024dv2 \([0, 0, 0, -15446739, -23366953478]\) \(616425416371016/2024451\) \(1338630974110729728\) \([2]\) \(24330240\) \(2.7010\) \(\Gamma_0(N)\)-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 453024dv1.