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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 102.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102.c1 | 102b5 | \([1, 0, 0, -27744, -1781010]\) | \(2361739090258884097/5202\) | \(5202\) | \([2]\) | \(128\) | \(0.84708\) | |
| 102.c2 | 102b3 | \([1, 0, 0, -1734, -27936]\) | \(576615941610337/27060804\) | \(27060804\) | \([2, 2]\) | \(64\) | \(0.50050\) | |
| 102.c3 | 102b6 | \([1, 0, 0, -1644, -30942]\) | \(-491411892194497/125563633938\) | \(-125563633938\) | \([2]\) | \(128\) | \(0.84708\) | |
| 102.c4 | 102b2 | \([1, 0, 0, -114, -396]\) | \(163936758817/30338064\) | \(30338064\) | \([2, 4]\) | \(32\) | \(0.15393\) | |
| 102.c5 | 102b1 | \([1, 0, 0, -34, 68]\) | \(4354703137/352512\) | \(352512\) | \([8]\) | \(16\) | \(-0.19264\) | \(\Gamma_0(N)\)-optimal |
| 102.c6 | 102b4 | \([1, 0, 0, 226, -2232]\) | \(1276229915423/2927177028\) | \(-2927177028\) | \([4]\) | \(64\) | \(0.50050\) |
Rank
sage: E.rank()
The elliptic curves in class 102.c have rank \(0\).
Complex multiplication
The elliptic curves in class 102.c do not have complex multiplication.Modular form 102.2.a.c
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.
