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SageMath
E = EllipticCurve("va1")
E.isogeny_class()
Elliptic curves in class 235200.va
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.va1 | 235200va7 | \([0, 1, 0, -505760033, 2754117780063]\) | \(29689921233686449/10380965400750\) | \(5002486572780899328000000000\) | \([2]\) | \(127401984\) | \(4.0164\) | |
| 235200.va2 | 235200va4 | \([0, 1, 0, -451664033, 3694482660063]\) | \(21145699168383889/2593080\) | \(1249580109496320000000\) | \([2]\) | \(42467328\) | \(3.4671\) | |
| 235200.va3 | 235200va6 | \([0, 1, 0, -211760033, -1154612219937]\) | \(2179252305146449/66177562500\) | \(31890325711104000000000000\) | \([2, 2]\) | \(63700992\) | \(3.6698\) | |
| 235200.va4 | 235200va3 | \([0, 1, 0, -210192033, -1173000155937]\) | \(2131200347946769/2058000\) | \(991730245632000000000\) | \([2]\) | \(31850496\) | \(3.3233\) | |
| 235200.va5 | 235200va2 | \([0, 1, 0, -28304033, 57396900063]\) | \(5203798902289/57153600\) | \(27541765678694400000000\) | \([2, 2]\) | \(21233664\) | \(3.1205\) | |
| 235200.va6 | 235200va5 | \([0, 1, 0, -6352033, 144173156063]\) | \(-58818484369/18600435000\) | \(-8963369276682240000000000\) | \([2]\) | \(42467328\) | \(3.4671\) | |
| 235200.va7 | 235200va1 | \([0, 1, 0, -3216033, -782171937]\) | \(7633736209/3870720\) | \(1865262437498880000000\) | \([2]\) | \(10616832\) | \(2.7740\) | \(\Gamma_0(N)\)-optimal |
| 235200.va8 | 235200va8 | \([0, 1, 0, 57151967, -3886489227937]\) | \(42841933504271/13565917968750\) | \(-6537284334000000000000000000\) | \([2]\) | \(127401984\) | \(4.0164\) |
Rank
sage: E.rank()
The elliptic curves in class 235200.va have rank \(0\).
Complex multiplication
The elliptic curves in class 235200.va do not have complex multiplication.Modular form 235200.2.a.va
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.
