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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 297024t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 297024.t2 | 297024t1 | \([0, -1, 0, -19864, 1083814]\) | \(13544585561654848/5980629291\) | \(382760274624\) | \([2]\) | \(589824\) | \(1.1814\) | \(\Gamma_0(N)\)-optimal |
| 297024.t1 | 297024t2 | \([0, -1, 0, -23049, 716265]\) | \(330627421369792/138380683077\) | \(566807277883392\) | \([2]\) | \(1179648\) | \(1.5280\) |
Rank
sage: E.rank()
The elliptic curves in class 297024t have rank \(1\).
Complex multiplication
The elliptic curves in class 297024t do not have complex multiplication.Modular form 297024.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
