Properties

Label 8400.ci
Number of curves $2$
Conductor $8400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ci1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8400.ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8400.ci1 8400cj2 \([0, 1, 0, -140208, 21333588]\) \(-7620530425/526848\) \(-21073920000000000\) \([]\) \(77760\) \(1.8832\)  
8400.ci2 8400cj1 \([0, 1, 0, 9792, 33588]\) \(2595575/1512\) \(-60480000000000\) \([]\) \(25920\) \(1.3339\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8400.ci have rank \(0\).

Complex multiplication

The elliptic curves in class 8400.ci do not have complex multiplication.

Modular form 8400.2.a.ci

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} - 6q^{11} + q^{13} - 3q^{17} + 4q^{19} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.