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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 15210.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15210.e1 | 15210j1 | \([1, -1, 0, -1290600, -565400250]\) | \(-2365581049/6750\) | \(-678367173765966750\) | \([]\) | \(314496\) | \(2.2932\) | \(\Gamma_0(N)\)-optimal |
15210.e2 | 15210j2 | \([1, -1, 0, 2565135, -2899662219]\) | \(18573478391/46875000\) | \(-4710883151152546875000\) | \([]\) | \(943488\) | \(2.8425\) |
Rank
sage: E.rank()
The elliptic curves in class 15210.e have rank \(0\).
Complex multiplication
The elliptic curves in class 15210.e do not have complex multiplication.Modular form 15210.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.