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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 147294cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 147294.u4 | 147294cj1 | \([1, -1, 0, -37858536, 95106809664]\) | \(-69967989877865233393/5060983303176192\) | \(-434060906359188967391232\) | \([2]\) | \(18579456\) | \(3.2852\) | \(\Gamma_0(N)\)-optimal |
| 147294.u3 | 147294cj2 | \([1, -1, 0, -615886056, 5883127578432]\) | \(301237516670332318563313/1421837758365696\) | \(121945509226361045385216\) | \([2, 2]\) | \(37158912\) | \(3.6318\) | |
| 147294.u1 | 147294cj3 | \([1, -1, 0, -9854165736, 376513670060352]\) | \(1233864675106127856683588593/27488595456\) | \(2357590203999346176\) | \([2]\) | \(74317824\) | \(3.9784\) | |
| 147294.u2 | 147294cj4 | \([1, -1, 0, -626046696, 5678977967424]\) | \(316393918884564908858353/20661539369919533568\) | \(1772060085646782476256649728\) | \([2]\) | \(74317824\) | \(3.9784\) |
Rank
sage: E.rank()
The elliptic curves in class 147294cj have rank \(1\).
Complex multiplication
The elliptic curves in class 147294cj do not have complex multiplication.Modular form 147294.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
