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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 76296.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76296.k1 | 76296b4 | \([0, -1, 0, -203552, 35415612]\) | \(37736227588/33\) | \(815656731648\) | \([2]\) | \(442368\) | \(1.5859\) | |
| 76296.k2 | 76296b3 | \([0, -1, 0, -30152, -1234212]\) | \(122657188/43923\) | \(1085639109823488\) | \([2]\) | \(442368\) | \(1.5859\) | |
| 76296.k3 | 76296b2 | \([0, -1, 0, -12812, 548340]\) | \(37642192/1089\) | \(6729168036096\) | \([2, 2]\) | \(221184\) | \(1.2394\) | |
| 76296.k4 | 76296b1 | \([0, -1, 0, 193, 28140]\) | \(2048/891\) | \(-344105183664\) | \([2]\) | \(110592\) | \(0.89278\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 76296.k have rank \(0\).
Complex multiplication
The elliptic curves in class 76296.k do not have complex multiplication.Modular form 76296.2.a.k
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
