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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 3234.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3234.t1 | 3234t3 | \([1, 0, 0, -17249, 870519]\) | \(4824238966273/66\) | \(7764834\) | \([2]\) | \(4608\) | \(0.87800\) | |
| 3234.t2 | 3234t2 | \([1, 0, 0, -1079, 13509]\) | \(1180932193/4356\) | \(512479044\) | \([2, 2]\) | \(2304\) | \(0.53143\) | |
| 3234.t3 | 3234t4 | \([1, 0, 0, -589, 25955]\) | \(-192100033/2371842\) | \(-279044839458\) | \([2]\) | \(4608\) | \(0.87800\) | |
| 3234.t4 | 3234t1 | \([1, 0, 0, -99, -15]\) | \(912673/528\) | \(62118672\) | \([2]\) | \(1152\) | \(0.18485\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3234.t have rank \(0\).
Complex multiplication
The elliptic curves in class 3234.t do not have complex multiplication.Modular form 3234.2.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.
