Properties

Label 395.a
Number of curves 2
Conductor 395
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("395.a1")
sage: E.isogeny_class()

Elliptic curves in class 395.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
395.a1 395c1 [0, -1, 1, -50, 156] 5 68 \(\Gamma_0(N)\)-optimal
395.a2 395c2 [0, -1, 1, 300, -5724] 1 340  

Rank

sage: E.rank()

The elliptic curves in class 395.a have rank \(0\).

Modular form 395.2.a.a

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

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.