Properties

Label 78400.gm
Number of curves $4$
Conductor $78400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("gm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 78400.gm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
78400.gm1 78400u4 [0, 0, 0, -1465100, -682570000] [2] 786432  
78400.gm2 78400u3 [0, 0, 0, -289100, 47334000] [2] 786432  
78400.gm3 78400u2 [0, 0, 0, -93100, -10290000] [2, 2] 393216  
78400.gm4 78400u1 [0, 0, 0, 4900, -686000] [2] 196608 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 78400.2.a.gm

sage: E.q_eigenform(10)
 
\( q - 3q^{9} + 4q^{11} - 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.