Properties

Label 95139.c
Number of curves 4
Conductor 95139
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("95139.c1")
sage: E.isogeny_class()

Elliptic curves in class 95139.c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
95139.c1 95139j4 [1, -1, 1, -1267259, 548870600] 2 1382400  
95139.c2 95139j2 [1, -1, 1, -99644, 3827918] 4 691200  
95139.c3 95139j1 [1, -1, 1, -56399, -5097850] 2 345600 \(\Gamma_0(N)\)-optimal
95139.c4 95139j3 [1, -1, 1, 376051, 29515448] 2 1382400  

Rank

sage: E.rank()

The elliptic curves in class 95139.c have rank \(0\).

Modular form 95139.2.a.c

sage: E.q_eigenform(10)
\( q - q^{2} - q^{4} + 2q^{5} + 4q^{7} + 3q^{8} - 2q^{10} + q^{11} + 2q^{13} - 4q^{14} - q^{16} - 2q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.