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SageMath
E = EllipticCurve("ii1")
E.isogeny_class()
Elliptic curves in class 277440.ii
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277440.ii1 | 277440ii3 | \([0, 1, 0, -185345, 30650655]\) | \(890277128/15\) | \(11864097914880\) | \([2]\) | \(1179648\) | \(1.6390\) | |
| 277440.ii2 | 277440ii4 | \([0, 1, 0, -46625, -3418977]\) | \(14172488/1875\) | \(1483012239360000\) | \([2]\) | \(1179648\) | \(1.6390\) | |
| 277440.ii3 | 277440ii2 | \([0, 1, 0, -11945, 444375]\) | \(1906624/225\) | \(22245183590400\) | \([2, 2]\) | \(589824\) | \(1.2924\) | |
| 277440.ii4 | 277440ii1 | \([0, 1, 0, 1060, 36018]\) | \(85184/405\) | \(-625645788480\) | \([2]\) | \(294912\) | \(0.94584\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277440.ii have rank \(1\).
Complex multiplication
The elliptic curves in class 277440.ii do not have complex multiplication.Modular form 277440.2.a.ii
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
