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Properties

Label 435344bv
Number of curves $2$
Conductor $435344$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bv1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 435344bv have rank \(0\).

Complex multiplication

The elliptic curves in class 435344bv do not have complex multiplication.

Modular form 435344.2.a.bv

Copy content sage:E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{7} + q^{9} - 6 q^{17} + 6 q^{19} + O(q^{20})\) 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 435344bv

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435344.bv2 435344bv1 \([0, -1, 0, 708392, -34111104]\) \(7953970437500/4703287687\) \(-23246716249293601792\) \([2]\) \(9031680\) \(2.4054\) \(\Gamma_0(N)\)-optimal*
435344.bv1 435344bv2 \([0, -1, 0, -2867648, -271560160]\) \(263822189935250/149429406721\) \(1477155236301994575872\) \([2]\) \(18063360\) \(2.7520\) \(\Gamma_0(N)\)-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 435344bv1.