Properties

Label 35301.c
Number of curves 6
Conductor 35301
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("35301.c1")
sage: E.isogeny_class()

Elliptic curves in class 35301.c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
35301.c1 35301e6 [1, 1, 1, -1317939, -582908538] 2 281600  
35301.c2 35301e4 [1, 1, 1, -82404, -9126084] 4 140800  
35301.c3 35301e3 [1, 1, 1, -65594, 6399632] 2 140800  
35301.c4 35301e5 [1, 1, 1, -57189, -14784330] 2 281600  
35301.c5 35301e2 [1, 1, 1, -6759, -48684] 4 70400  
35301.c6 35301e1 [1, 1, 1, 1646, -4978] 2 35200 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 35301.c have rank \(0\).

Modular form 35301.2.a.c

sage: E.q_eigenform(10)
\( q - q^{2} - q^{3} - q^{4} - 2q^{5} + q^{6} + q^{7} + 3q^{8} + q^{9} + 2q^{10} - 4q^{11} + q^{12} + 2q^{13} - q^{14} + 2q^{15} - q^{16} + 6q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.