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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 363888r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 363888.r3 | 363888r1 | \([0, 0, 0, -3029151, -2029207714]\) | \(350104249168/2793\) | \(24522234154612992\) | \([2]\) | \(7372800\) | \(2.3170\) | \(\Gamma_0(N)\)-optimal |
| 363888.r2 | 363888r2 | \([0, 0, 0, -3094131, -1937598910]\) | \(93280467172/7800849\) | \(273962399975336346624\) | \([2, 2]\) | \(14745600\) | \(2.6636\) | |
| 363888.r1 | 363888r3 | \([0, 0, 0, -10501851, 10870348970]\) | \(1823652903746/328593657\) | \(23080130608448511166464\) | \([4]\) | \(29491200\) | \(3.0101\) | |
| 363888.r4 | 363888r4 | \([0, 0, 0, 3273909, -8882583334]\) | \(55251546334/517244049\) | \(-36330768878361950619648\) | \([2]\) | \(29491200\) | \(3.0101\) |
Rank
sage: E.rank()
The elliptic curves in class 363888r have rank \(0\).
Complex multiplication
The elliptic curves in class 363888r do not have complex multiplication.Modular form 363888.2.a.r
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.
