Properties

Label 493680cv
Number of curves $2$
Conductor $493680$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cv1")
 
E.isogeny_class()
 

Elliptic curves in class 493680cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
493680.cv1 493680cv1 \([0, -1, 0, -198480, 34718400]\) \(-119168121961/2524500\) \(-18318564329472000\) \([]\) \(4147200\) \(1.9110\) \(\Gamma_0(N)\)-optimal
493680.cv2 493680cv2 \([0, -1, 0, 817920, 155873280]\) \(8339492177639/6277634880\) \(-45552488962652897280\) \([]\) \(12441600\) \(2.4603\)  

Rank

sage: E.rank()
 

The elliptic curves in class 493680cv have rank \(1\).

Complex multiplication

The elliptic curves in class 493680cv do not have complex multiplication.

Modular form 493680.2.a.cv

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - q^{7} + q^{9} + q^{13} - q^{15} + q^{17} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.