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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 243360bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 243360.bg3 | 243360bg1 | \([0, 0, 0, -2436104073, -46276591615072]\) | \(7099759044484031233216/577161945398025\) | \(129976639645179080350209600\) | \([2, 2]\) | \(144506880\) | \(4.0559\) | \(\Gamma_0(N)\)-optimal |
| 243360.bg2 | 243360bg2 | \([0, 0, 0, -2603185923, -39565348113382]\) | \(1082883335268084577352/251301565117746585\) | \(452744096966454285490076766720\) | \([2]\) | \(289013760\) | \(4.4025\) | |
| 243360.bg4 | 243360bg3 | \([0, 0, 0, -2269782723, -52866476351962]\) | \(-717825640026599866952/254764560814329735\) | \(-458983018951335851227153067520\) | \([2]\) | \(289013760\) | \(4.4025\) | |
| 243360.bg1 | 243360bg4 | \([0, 0, 0, -38976904668, -2961823222129408]\) | \(454357982636417669333824/3003024375\) | \(43281912969880266240000\) | \([2]\) | \(289013760\) | \(4.4025\) |
Rank
sage: E.rank()
The elliptic curves in class 243360bg have rank \(0\).
Complex multiplication
The elliptic curves in class 243360bg do not have complex multiplication.Modular form 243360.2.a.bg
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
