Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7800.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7800.h1 7800l2 \([0, -1, 0, -5008, 136012]\) \(434163602/7605\) \(243360000000\) \([2]\) \(9216\) \(0.98134\)  
7800.h2 7800l1 \([0, -1, 0, -8, 6012]\) \(-4/975\) \(-15600000000\) \([2]\) \(4608\) \(0.63476\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7800.2.a.h

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