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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 294.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 294.g1 | 294c3 | \([1, 0, 0, -65857, -6510547]\) | \(268498407453697/252\) | \(29647548\) | \([2]\) | \(768\) | \(1.1621\) | |
| 294.g2 | 294c5 | \([1, 0, 0, -44787, 3609423]\) | \(84448510979617/933897762\) | \(109872137801538\) | \([2]\) | \(1536\) | \(1.5086\) | |
| 294.g3 | 294c4 | \([1, 0, 0, -5097, -49995]\) | \(124475734657/63011844\) | \(7413280434756\) | \([2, 2]\) | \(768\) | \(1.1621\) | |
| 294.g4 | 294c2 | \([1, 0, 0, -4117, -101935]\) | \(65597103937/63504\) | \(7471182096\) | \([2, 2]\) | \(384\) | \(0.81548\) | |
| 294.g5 | 294c1 | \([1, 0, 0, -197, -2367]\) | \(-7189057/16128\) | \(-1897443072\) | \([4]\) | \(192\) | \(0.46891\) | \(\Gamma_0(N)\)-optimal |
| 294.g6 | 294c6 | \([1, 0, 0, 18913, -381333]\) | \(6359387729183/4218578658\) | \(-496311560535042\) | \([2]\) | \(1536\) | \(1.5086\) |
Rank
sage: E.rank()
The elliptic curves in class 294.g have rank \(0\).
Complex multiplication
The elliptic curves in class 294.g do not have complex multiplication.Modular form 294.2.a.g
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
