Properties

Label 78400.eb
Number of curves $3$
Conductor $78400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("eb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 78400.eb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78400.eb1 78400bq3 \([0, -1, 0, -643533, 208075687]\) \(-250523582464/13671875\) \(-1608482421875000000\) \([]\) \(995328\) \(2.2517\)  
78400.eb2 78400bq1 \([0, -1, 0, -6533, -223313]\) \(-262144/35\) \(-4117715000000\) \([]\) \(110592\) \(1.1531\) \(\Gamma_0(N)\)-optimal
78400.eb3 78400bq2 \([0, -1, 0, 42467, 560687]\) \(71991296/42875\) \(-5044200875000000\) \([]\) \(331776\) \(1.7024\)  

Rank

sage: E.rank()
 

The elliptic curves in class 78400.eb have rank \(0\).

Complex multiplication

The elliptic curves in class 78400.eb do not have complex multiplication.

Modular form 78400.2.a.eb

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{9} + 3q^{11} - 5q^{13} + 3q^{17} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.