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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 3570.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3570.t1 | 3570t5 | \([1, 1, 1, -1742580, -886120275]\) | \(585196747116290735872321/836876053125000\) | \(836876053125000\) | \([2]\) | \(73728\) | \(2.1347\) | |
| 3570.t2 | 3570t4 | \([1, 1, 1, -252620, 48757805]\) | \(1782900110862842086081/328139630024640\) | \(328139630024640\) | \([4]\) | \(36864\) | \(1.7881\) | |
| 3570.t3 | 3570t3 | \([1, 1, 1, -109900, -13616083]\) | \(146796951366228945601/5397929064360000\) | \(5397929064360000\) | \([2, 2]\) | \(36864\) | \(1.7881\) | |
| 3570.t4 | 3570t2 | \([1, 1, 1, -17420, 588845]\) | \(584614687782041281/184812061593600\) | \(184812061593600\) | \([2, 4]\) | \(18432\) | \(1.4415\) | |
| 3570.t5 | 3570t1 | \([1, 1, 1, 3060, 64557]\) | \(3168685387909439/3563732336640\) | \(-3563732336640\) | \([4]\) | \(9216\) | \(1.0949\) | \(\Gamma_0(N)\)-optimal |
| 3570.t6 | 3570t6 | \([1, 1, 1, 43100, -48377683]\) | \(8854313460877886399/1016927675429790600\) | \(-1016927675429790600\) | \([2]\) | \(73728\) | \(2.1347\) |
Rank
sage: E.rank()
The elliptic curves in class 3570.t have rank \(0\).
Complex multiplication
The elliptic curves in class 3570.t do not have complex multiplication.Modular form 3570.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
