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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 215475.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 215475.t1 | 215475p6 | \([1, 0, 0, -85235238, -302844873033]\) | \(908031902324522977/161726530797\) | \(12197235537339637078125\) | \([2]\) | \(22020096\) | \(3.2423\) | |
| 215475.t2 | 215475p4 | \([1, 0, 0, -5868613, -3712063408]\) | \(296380748763217/92608836489\) | \(6984455710072400015625\) | \([2, 2]\) | \(11010048\) | \(2.8958\) | |
| 215475.t3 | 215475p2 | \([1, 0, 0, -2298488, 1296821967]\) | \(17806161424897/668584449\) | \(50423897432706890625\) | \([2, 2]\) | \(5505024\) | \(2.5492\) | |
| 215475.t4 | 215475p1 | \([1, 0, 0, -2277363, 1322615592]\) | \(17319700013617/25857\) | \(1950106254890625\) | \([2]\) | \(2752512\) | \(2.2026\) | \(\Gamma_0(N)\)-optimal |
| 215475.t5 | 215475p3 | \([1, 0, 0, 933637, 4654999842]\) | \(1193377118543/124806800313\) | \(-9412790422062362765625\) | \([2]\) | \(11010048\) | \(2.8958\) | |
| 215475.t6 | 215475p5 | \([1, 0, 0, 16376012, -25133637283]\) | \(6439735268725823/7345472585373\) | \(-553987393505182261828125\) | \([2]\) | \(22020096\) | \(3.2423\) |
Rank
sage: E.rank()
The elliptic curves in class 215475.t have rank \(0\).
Complex multiplication
The elliptic curves in class 215475.t do not have complex multiplication.Modular form 215475.2.a.t
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
