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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 222024i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 222024.b4 | 222024i1 | \([0, -1, 0, 561, 139824]\) | \(2048/891\) | \(-8479801264176\) | \([2]\) | \(580608\) | \(1.1598\) | \(\Gamma_0(N)\)-optimal |
| 222024.b3 | 222024i2 | \([0, -1, 0, -37284, 2713284]\) | \(37642192/1089\) | \(165827224721664\) | \([2, 2]\) | \(1161216\) | \(1.5064\) | |
| 222024.b1 | 222024i3 | \([0, -1, 0, -592344, 175669980]\) | \(37736227588/33\) | \(20100269663232\) | \([2]\) | \(2322432\) | \(1.8530\) | |
| 222024.b2 | 222024i4 | \([0, -1, 0, -87744, -6147492]\) | \(122657188/43923\) | \(26753458921761792\) | \([2]\) | \(2322432\) | \(1.8530\) |
Rank
sage: E.rank()
The elliptic curves in class 222024i have rank \(1\).
Complex multiplication
The elliptic curves in class 222024i do not have complex multiplication.Modular form 222024.2.a.i
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.
