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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 302005j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 302005.j3 | 302005j1 | \([1, -1, 0, -283916255, -1841266956800]\) | \(104857852278310619039721/47155625\) | \(1138222152175625\) | \([2]\) | \(20348928\) | \(3.1324\) | \(\Gamma_0(N)\)-optimal |
| 302005.j2 | 302005j2 | \([1, -1, 0, -283917700, -1841247276189]\) | \(104859453317683374662841/2223652969140625\) | \(53673576974686706640625\) | \([2, 2]\) | \(40697856\) | \(3.4790\) | |
| 302005.j1 | 302005j3 | \([1, -1, 0, -293852075, -1705470199314]\) | \(116256292809537371612841/15216540068579856875\) | \(367290285846611027330436875\) | \([2]\) | \(81395712\) | \(3.8256\) | |
| 302005.j4 | 302005j4 | \([1, -1, 0, -274006445, -1975764811300]\) | \(-94256762600623910012361/15323275604248046875\) | \(-369866622203553924560546875\) | \([2]\) | \(81395712\) | \(3.8256\) |
Rank
sage: E.rank()
The elliptic curves in class 302005j have rank \(1\).
Complex multiplication
The elliptic curves in class 302005j do not have complex multiplication.Modular form 302005.2.a.j
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.
