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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 38115.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38115.t1 | 38115l4 | \([1, -1, 0, -626194080, 6031465104825]\) | \(21026497979043461623321/161783881875\) | \(208938701342042161875\) | \([2]\) | \(7372800\) | \(3.4915\) | |
| 38115.t2 | 38115l2 | \([1, -1, 0, -39163185, 94117226616]\) | \(5143681768032498601/14238434358225\) | \(18388481902356659195025\) | \([2, 2]\) | \(3686400\) | \(3.1450\) | |
| 38115.t3 | 38115l3 | \([1, -1, 0, -23726610, 169055623611]\) | \(-1143792273008057401/8897444448004035\) | \(-11490764510554097185254915\) | \([2]\) | \(7372800\) | \(3.4915\) | |
| 38115.t4 | 38115l1 | \([1, -1, 0, -3438540, 168555195]\) | \(3481467828171481/2005331497785\) | \(2589821396616121948665\) | \([2]\) | \(1843200\) | \(2.7984\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38115.t have rank \(1\).
Complex multiplication
The elliptic curves in class 38115.t do not have complex multiplication.Modular form 38115.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
