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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 60840.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60840.t1 | 60840s1 | \([0, 0, 0, -88569858, -285543252943]\) | \(621217777580032/74733890625\) | \(9243900748547670143250000\) | \([2]\) | \(11741184\) | \(3.5212\) | \(\Gamma_0(N)\)-optimal |
| 60840.t2 | 60840s2 | \([0, 0, 0, 127647897, -1462157032102]\) | \(116227003261808/533935546875\) | \(-1056687328366217437500000000\) | \([2]\) | \(23482368\) | \(3.8678\) |
Rank
sage: E.rank()
The elliptic curves in class 60840.t have rank \(1\).
Complex multiplication
The elliptic curves in class 60840.t do not have complex multiplication.Modular form 60840.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
