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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 363888cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 363888.cj2 | 363888cj1 | \([0, 0, 0, -806862075, 8821593641002]\) | \(11165451838341046875/572244736\) | \(2977331033390183350272\) | \([2]\) | \(79626240\) | \(3.5934\) | \(\Gamma_0(N)\)-optimal |
| 363888.cj3 | 363888cj2 | \([0, 0, 0, -805475835, 8853415889194]\) | \(-11108001800138902875/79947274872976\) | \(-415957522262444496159178752\) | \([2]\) | \(159252480\) | \(3.9400\) | |
| 363888.cj1 | 363888cj3 | \([0, 0, 0, -879033195, 7149790967706]\) | \(19804628171203875/5638671302656\) | \(21386987962047584972883099648\) | \([2]\) | \(238878720\) | \(4.1427\) | |
| 363888.cj4 | 363888cj4 | \([0, 0, 0, 2314863765, 47164848420762]\) | \(361682234074684125/462672528510976\) | \(-1754876506629036836211243614208\) | \([2]\) | \(477757440\) | \(4.4893\) |
Rank
sage: E.rank()
The elliptic curves in class 363888cj have rank \(1\).
Complex multiplication
The elliptic curves in class 363888cj do not have complex multiplication.Modular form 363888.2.a.cj
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
