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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 2520.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2520.t1 | 2520j3 | \([0, 0, 0, -4107, -101194]\) | \(10262905636/13125\) | \(9797760000\) | \([2]\) | \(2048\) | \(0.82502\) | |
| 2520.t2 | 2520j4 | \([0, 0, 0, -3027, 63614]\) | \(4108974916/36015\) | \(26885053440\) | \([4]\) | \(2048\) | \(0.82502\) | |
| 2520.t3 | 2520j2 | \([0, 0, 0, -327, -646]\) | \(20720464/11025\) | \(2057529600\) | \([2, 2]\) | \(1024\) | \(0.47845\) | |
| 2520.t4 | 2520j1 | \([0, 0, 0, 78, -79]\) | \(4499456/2835\) | \(-33067440\) | \([2]\) | \(512\) | \(0.13187\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2520.t have rank \(0\).
Complex multiplication
The elliptic curves in class 2520.t do not have complex multiplication.Modular form 2520.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
