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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 244398c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
244398.c4 | 244398c1 | \([1, 1, 0, -340951, 25208149]\) | \(29609739866953/15259926528\) | \(2259016789647163392\) | \([2]\) | \(5913600\) | \(2.2139\) | \(\Gamma_0(N)\)-optimal |
244398.c2 | 244398c2 | \([1, 1, 0, -3049431, -2032694955]\) | \(21184262604460873/216872764416\) | \(32104952480210125824\) | \([2, 2]\) | \(11827200\) | \(2.5605\) | |
244398.c3 | 244398c3 | \([1, 1, 0, -764151, -5005844235]\) | \(-333345918055753/72923718045024\) | \(-10795327429980469866336\) | \([2]\) | \(23654400\) | \(2.9071\) | |
244398.c1 | 244398c4 | \([1, 1, 0, -48670391, -130711174731]\) | \(86129359107301290313/9166294368\) | \(1356940535602573152\) | \([2]\) | \(23654400\) | \(2.9071\) |
Rank
sage: E.rank()
The elliptic curves in class 244398c have rank \(1\).
Complex multiplication
The elliptic curves in class 244398c do not have complex multiplication.Modular form 244398.2.a.c
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.