Properties

Label 7800.j
Number of curves $2$
Conductor $7800$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 7800.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7800.j1 7800b2 \([0, -1, 0, -1508, 21012]\) \(94875856/9477\) \(37908000000\) \([2]\) \(7680\) \(0.76625\)  
7800.j2 7800b1 \([0, -1, 0, 117, 1512]\) \(702464/4563\) \(-1140750000\) \([2]\) \(3840\) \(0.41968\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7800.j have rank \(0\).

Complex multiplication

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

Modular form 7800.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{3} + 4 q^{7} + q^{9} - 2 q^{11} + q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 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.