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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 9744.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9744.l1 | 9744q3 | \([0, 1, 0, -3273984, -2281239180]\) | \(947531277805646290177/38367\) | \(157151232\) | \([2]\) | \(98304\) | \(1.9838\) | |
| 9744.l2 | 9744q5 | \([0, 1, 0, -679504, 175033940]\) | \(8471112631466271697/1662662681263647\) | \(6810266342455898112\) | \([4]\) | \(196608\) | \(2.3304\) | |
| 9744.l3 | 9744q4 | \([0, 1, 0, -208544, -34260684]\) | \(244883173420511137/18418027974129\) | \(75440242582032384\) | \([2, 4]\) | \(98304\) | \(1.9838\) | |
| 9744.l4 | 9744q2 | \([0, 1, 0, -204624, -35695404]\) | \(231331938231569617/1472026689\) | \(6029421318144\) | \([2, 2]\) | \(49152\) | \(1.6372\) | |
| 9744.l5 | 9744q1 | \([0, 1, 0, -12544, -583180]\) | \(-53297461115137/4513839183\) | \(-18488685293568\) | \([2]\) | \(24576\) | \(1.2907\) | \(\Gamma_0(N)\)-optimal |
| 9744.l6 | 9744q6 | \([0, 1, 0, 199696, -151670508]\) | \(215015459663151503/2552757445339983\) | \(-10456094496112570368\) | \([4]\) | \(196608\) | \(2.3304\) |
Rank
sage: E.rank()
The elliptic curves in class 9744.l have rank \(0\).
Complex multiplication
The elliptic curves in class 9744.l do not have complex multiplication.Modular form 9744.2.a.l
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.
