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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 259920.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259920.z1 | 259920z4 | \([0, 0, 0, -388711443, 2848459445458]\) | \(46237740924063961/1806561830400\) | \(253782640715245504797081600\) | \([2]\) | \(59719680\) | \(3.8338\) | |
| 259920.z2 | 259920z2 | \([0, 0, 0, -57313443, -165815899742]\) | \(148212258825961/1218375000\) | \(171155185324033536000000\) | \([2]\) | \(19906560\) | \(3.2845\) | |
| 259920.z3 | 259920z1 | \([0, 0, 0, -1170723, -6022490078]\) | \(-1263214441/110808000\) | \(-15566113696838418432000\) | \([2]\) | \(9953280\) | \(2.9379\) | \(\Gamma_0(N)\)-optimal |
| 259920.z4 | 259920z3 | \([0, 0, 0, 10525677, 161673475282]\) | \(918046641959/80912056320\) | \(-11366383908401139972833280\) | \([2]\) | \(29859840\) | \(3.4872\) |
Rank
sage: E.rank()
The elliptic curves in class 259920.z have rank \(0\).
Complex multiplication
The elliptic curves in class 259920.z do not have complex multiplication.Modular form 259920.2.a.z
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
