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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 4851.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4851.t1 | 4851l3 | \([0, 0, 1, -3448767, -2465153091]\) | \(-52893159101157376/11\) | \(-943427331\) | \([]\) | \(54000\) | \(2.0190\) | |
| 4851.t2 | 4851l2 | \([0, 0, 1, -4557, -214461]\) | \(-122023936/161051\) | \(-13812719553171\) | \([]\) | \(10800\) | \(1.2143\) | |
| 4851.t3 | 4851l1 | \([0, 0, 1, -147, 1629]\) | \(-4096/11\) | \(-943427331\) | \([]\) | \(2160\) | \(0.40953\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4851.t have rank \(1\).
Complex multiplication
The elliptic curves in class 4851.t do not have complex multiplication.Modular form 4851.2.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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
