Properties

Label 397800cv
Number of curves $2$
Conductor $397800$
CM no
Rank $1$
Graph

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

Elliptic curves in class 397800cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
397800.cv2 397800cv1 \([0, 0, 0, 2850, -14375]\) \(14047232/8619\) \(-1570812750000\) \([2]\) \(524288\) \(1.0294\) \(\Gamma_0(N)\)-optimal
397800.cv1 397800cv2 \([0, 0, 0, -11775, -116750]\) \(61918288/33813\) \(98598708000000\) \([2]\) \(1048576\) \(1.3760\)  

Rank

sage: E.rank()
 

The elliptic curves in class 397800cv have rank \(1\).

Complex multiplication

The elliptic curves in class 397800cv do not have complex multiplication.

Modular form 397800.2.a.cv

sage: E.q_eigenform(10)
 
\(q + 2 q^{7} - 4 q^{11} - q^{13} + q^{17} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.