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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 2310k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2310.j4 | 2310k1 | \([1, 0, 1, 192, -194]\) | \(788632918919/475398000\) | \(-475398000\) | \([2]\) | \(1536\) | \(0.35423\) | \(\Gamma_0(N)\)-optimal |
2310.j3 | 2310k2 | \([1, 0, 1, -788, -1762]\) | \(54014438633401/30015562500\) | \(30015562500\) | \([2, 2]\) | \(3072\) | \(0.70080\) | |
2310.j1 | 2310k3 | \([1, 0, 1, -9538, -358762]\) | \(95946737295893401/168104301750\) | \(168104301750\) | \([2]\) | \(6144\) | \(1.0474\) | |
2310.j2 | 2310k4 | \([1, 0, 1, -7718, 258806]\) | \(50834334659676121/338378906250\) | \(338378906250\) | \([2]\) | \(6144\) | \(1.0474\) |
Rank
sage: E.rank()
The elliptic curves in class 2310k have rank \(1\).
Complex multiplication
The elliptic curves in class 2310k do not have complex multiplication.Modular form 2310.2.a.k
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.