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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 23064.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23064.i1 | 23064m6 | \([0, 1, 0, -369344, 86272992]\) | \(3065617154/9\) | \(16358467848192\) | \([2]\) | \(115200\) | \(1.7648\) | |
| 23064.i2 | 23064m4 | \([0, 1, 0, -61824, -5936880]\) | \(28756228/3\) | \(2726411308032\) | \([2]\) | \(57600\) | \(1.4182\) | |
| 23064.i3 | 23064m3 | \([0, 1, 0, -23384, 1305216]\) | \(1556068/81\) | \(73613105316864\) | \([2, 2]\) | \(57600\) | \(1.4182\) | |
| 23064.i4 | 23064m2 | \([0, 1, 0, -4164, -78624]\) | \(35152/9\) | \(2044808481024\) | \([2, 2]\) | \(28800\) | \(1.0716\) | |
| 23064.i5 | 23064m1 | \([0, 1, 0, 641, -7510]\) | \(2048/3\) | \(-42600176688\) | \([2]\) | \(14400\) | \(0.72507\) | \(\Gamma_0(N)\)-optimal |
| 23064.i6 | 23064m5 | \([0, 1, 0, 15056, 5210720]\) | \(207646/6561\) | \(-11925323061331968\) | \([2]\) | \(115200\) | \(1.7648\) |
Rank
sage: E.rank()
The elliptic curves in class 23064.i have rank \(0\).
Complex multiplication
The elliptic curves in class 23064.i do not have complex multiplication.Modular form 23064.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
