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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 11760.cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11760.cl1 | 11760co7 | \([0, 1, 0, -5057600, 2752600500]\) | \(29689921233686449/10380965400750\) | \(5002486572780899328000\) | \([2]\) | \(663552\) | \(2.8651\) | |
| 11760.cl2 | 11760co4 | \([0, 1, 0, -4516640, 3693127668]\) | \(21145699168383889/2593080\) | \(1249580109496320\) | \([2]\) | \(221184\) | \(2.3158\) | |
| 11760.cl3 | 11760co6 | \([0, 1, 0, -2117600, -1155247500]\) | \(2179252305146449/66177562500\) | \(31890325711104000000\) | \([2, 2]\) | \(331776\) | \(2.5186\) | |
| 11760.cl4 | 11760co3 | \([0, 1, 0, -2101920, -1173630732]\) | \(2131200347946769/2058000\) | \(991730245632000\) | \([2]\) | \(165888\) | \(2.1720\) | |
| 11760.cl5 | 11760co2 | \([0, 1, 0, -283040, 57311988]\) | \(5203798902289/57153600\) | \(27541765678694400\) | \([2, 2]\) | \(110592\) | \(1.9692\) | |
| 11760.cl6 | 11760co5 | \([0, 1, 0, -63520, 144154100]\) | \(-58818484369/18600435000\) | \(-8963369276682240000\) | \([4]\) | \(221184\) | \(2.3158\) | |
| 11760.cl7 | 11760co1 | \([0, 1, 0, -32160, -791820]\) | \(7633736209/3870720\) | \(1865262437498880\) | \([2]\) | \(55296\) | \(1.6227\) | \(\Gamma_0(N)\)-optimal |
| 11760.cl8 | 11760co8 | \([0, 1, 0, 571520, -3886317772]\) | \(42841933504271/13565917968750\) | \(-6537284334000000000000\) | \([4]\) | \(663552\) | \(2.8651\) |
Rank
sage: E.rank()
The elliptic curves in class 11760.cl have rank \(1\).
Complex multiplication
The elliptic curves in class 11760.cl do not have complex multiplication.Modular form 11760.2.a.cl
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
