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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 24843.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24843.p1 | 24843d6 | \([1, 1, 0, -6492476, 6364717689]\) | \(53297461115137/147\) | \(83476780050027\) | \([2]\) | \(442368\) | \(2.3296\) | |
| 24843.p2 | 24843d4 | \([1, 1, 0, -405941, 99238560]\) | \(13027640977/21609\) | \(12271086667353969\) | \([2, 2]\) | \(221184\) | \(1.9831\) | |
| 24843.p3 | 24843d3 | \([1, 1, 0, -323131, -70406006]\) | \(6570725617/45927\) | \(26080531138487007\) | \([2]\) | \(221184\) | \(1.9831\) | |
| 24843.p4 | 24843d5 | \([1, 1, 0, -281726, 161271531]\) | \(-4354703137/17294403\) | \(-9820959696105626523\) | \([2]\) | \(442368\) | \(2.3296\) | |
| 24843.p5 | 24843d2 | \([1, 1, 0, -33296, 487635]\) | \(7189057/3969\) | \(2253873061350729\) | \([2, 2]\) | \(110592\) | \(1.6365\) | |
| 24843.p6 | 24843d1 | \([1, 1, 0, 8109, 65304]\) | \(103823/63\) | \(-35775762878583\) | \([2]\) | \(55296\) | \(1.2899\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24843.p have rank \(0\).
Complex multiplication
The elliptic curves in class 24843.p do not have complex multiplication.Modular form 24843.2.a.p
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
