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SageMath
sage: E = EllipticCurve("33150.l1")
sage: E.isogeny_class()
Elliptic curves in class 33150b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
33150.l7 | 33150b1 | [1, 1, 0, -52403650, 140576384500] | [2] | 6635520 | \(\Gamma_0(N)\)-optimal |
33150.l6 | 33150b2 | [1, 1, 0, -138931650, -443401087500] | [2, 2] | 13271040 | |
33150.l5 | 33150b3 | [1, 1, 0, -644819650, -6261614367500] | [2] | 19906560 | |
33150.l8 | 33150b4 | [1, 1, 0, 372020350, -2946554935500] | [2] | 26542080 | |
33150.l4 | 33150b5 | [1, 1, 0, -2034331650, -35313074887500] | [2] | 26542080 | |
33150.l2 | 33150b6 | [1, 1, 0, -10298437650, -402262678345500] | [2, 2] | 39813120 | |
33150.l3 | 33150b7 | [1, 1, 0, -10279763150, -403794192765000] | [2] | 79626240 | |
33150.l1 | 33150b8 | [1, 1, 0, -164775000150, -25744606186158000] | [2] | 79626240 |
Rank
sage: E.rank()
The elliptic curves in class 33150b have rank \(1\).
Modular form 33150.2.a.l
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.