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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 76296.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76296.a1 | 76296d1 | \([0, -1, 0, -2316720, -1356473124]\) | \(55635379958596/24057\) | \(594613757371392\) | \([2]\) | \(1548288\) | \(2.1773\) | \(\Gamma_0(N)\)-optimal |
| 76296.a2 | 76296d2 | \([0, -1, 0, -2305160, -1370691924]\) | \(-27403349188178/578739249\) | \(-28609246322167154688\) | \([2]\) | \(3096576\) | \(2.5239\) |
Rank
sage: E.rank()
The elliptic curves in class 76296.a have rank \(0\).
Complex multiplication
The elliptic curves in class 76296.a do not have complex multiplication.Modular form 76296.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
