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SageMath
sage: E = EllipticCurve("m1")
sage: E.isogeny_class()
Elliptic curves in class 23520.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
23520.m1 | 23520bf4 | [0, -1, 0, -5000940016, 136122808277716] | [4] | 10321920 | |
23520.m2 | 23520bf3 | [0, -1, 0, -313630641, 2111674775841] | [2] | 10321920 | |
23520.m3 | 23520bf1 | [0, -1, 0, -312558766, 2126996800216] | [2, 2] | 5160960 | \(\Gamma_0(N)\)-optimal |
23520.m4 | 23520bf2 | [0, -1, 0, -311487136, 2142304820440] | [2] | 10321920 |
Rank
sage: E.rank()
The elliptic curves in class 23520.m have rank \(1\).
Complex multiplication
The elliptic curves in class 23520.m do not have complex multiplication.Modular form 23520.2.a.m
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.