Properties

Label 7800.s
Number of curves $2$
Conductor $7800$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7800.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7800.s1 7800i1 \([0, 1, 0, -16283, 745938]\) \(1909913257984/129730653\) \(32432663250000\) \([2]\) \(19200\) \(1.3411\) \(\Gamma_0(N)\)-optimal
7800.s2 7800i2 \([0, 1, 0, 14092, 3236688]\) \(77366117936/1172914587\) \(-4691658348000000\) \([2]\) \(38400\) \(1.6877\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7800.s have rank \(1\).

Complex multiplication

The elliptic curves in class 7800.s do not have complex multiplication.

Modular form 7800.2.a.s

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} - 2 q^{11} + q^{13} - 2 q^{17} + 8 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.