Properties

Label 200400m
Number of curves 2
Conductor 200400
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("200400.bs1")
sage: E.isogeny_class()

Elliptic curves in class 200400m

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
200400.bs2 200400m1 [0, 1, 0, -1808, 122388] 2 442368 \(\Gamma_0(N)\)-optimal
200400.bs1 200400m2 [0, 1, 0, -49808, 4250388] 2 884736  

Rank

sage: E.rank()

The elliptic curves in class 200400m have rank \(0\).

Modular form None

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.