Properties

Label 1400.g
Number of curves $4$
Conductor $1400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1400.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1400.g1 1400a4 [0, 0, 0, -7475, 248750] [2] 1024  
1400.g2 1400a3 [0, 0, 0, -1475, -17250] [2] 1024  
1400.g3 1400a2 [0, 0, 0, -475, 3750] [2, 2] 512  
1400.g4 1400a1 [0, 0, 0, 25, 250] [2] 256 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1400.g have rank \(0\).

Complex multiplication

The elliptic curves in class 1400.g do not have complex multiplication.

Modular form 1400.2.a.g

sage: E.q_eigenform(10)
 
\( q + q^{7} - 3q^{9} - 4q^{11} - 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20}) \)

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.