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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 242550.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242550.ci1 | 242550ci3 | \([1, -1, 0, -1014349842, 12434793555316]\) | \(86129359107301290313/9166294368\) | \(12283711123242289500000\) | \([2]\) | \(94371840\) | \(3.6663\) | |
| 242550.ci2 | 242550ci2 | \([1, -1, 0, -63553842, 193295055316]\) | \(21184262604460873/216872764416\) | \(290630246164174224000000\) | \([2, 2]\) | \(47185920\) | \(3.3197\) | |
| 242550.ci3 | 242550ci4 | \([1, -1, 0, -15925842, 476253003316]\) | \(-333345918055753/72923718045024\) | \(-97724756650303309873500000\) | \([2]\) | \(94371840\) | \(3.6663\) | |
| 242550.ci4 | 242550ci1 | \([1, -1, 0, -7105842, -2410160684]\) | \(29609739866953/15259926528\) | \(20449761016430592000000\) | \([2]\) | \(23592960\) | \(2.9731\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 242550.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 242550.ci do not have complex multiplication.Modular form 242550.2.a.ci
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
