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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 14994.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14994.i1 | 14994bh5 | \([1, -1, 0, -12235113, -16469463389]\) | \(2361739090258884097/5202\) | \(446155361442\) | \([2]\) | \(393216\) | \(2.3693\) | |
| 14994.i2 | 14994bh3 | \([1, -1, 0, -764703, -257185895]\) | \(576615941610337/27060804\) | \(2320900190221284\) | \([2, 2]\) | \(196608\) | \(2.0228\) | |
| 14994.i3 | 14994bh6 | \([1, -1, 0, -725013, -285103841]\) | \(-491411892194497/125563633938\) | \(-10769105821526214498\) | \([2]\) | \(393216\) | \(2.3693\) | |
| 14994.i4 | 14994bh2 | \([1, -1, 0, -50283, -3566795]\) | \(163936758817/30338064\) | \(2601978067929744\) | \([2, 2]\) | \(98304\) | \(1.6762\) | |
| 14994.i5 | 14994bh1 | \([1, -1, 0, -15003, 659749]\) | \(4354703137/352512\) | \(30233586845952\) | \([2]\) | \(49152\) | \(1.3296\) | \(\Gamma_0(N)\)-optimal |
| 14994.i6 | 14994bh4 | \([1, -1, 0, 99657, -20869871]\) | \(1276229915423/2927177028\) | \(-251052619171868388\) | \([2]\) | \(196608\) | \(2.0228\) |
Rank
sage: E.rank()
The elliptic curves in class 14994.i have rank \(0\).
Complex multiplication
The elliptic curves in class 14994.i do not have complex multiplication.Modular form 14994.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
