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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 6776a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6776.e3 | 6776a1 | \([0, 0, 0, -3146, 67881]\) | \(121485312/77\) | \(2182563152\) | \([4]\) | \(3840\) | \(0.73318\) | \(\Gamma_0(N)\)-optimal |
| 6776.e2 | 6776a2 | \([0, 0, 0, -3751, 39930]\) | \(12869712/5929\) | \(2688917803264\) | \([2, 2]\) | \(7680\) | \(1.0798\) | |
| 6776.e1 | 6776a3 | \([0, 0, 0, -30371, -2009810]\) | \(1707831108/26411\) | \(47911626312704\) | \([2]\) | \(15360\) | \(1.4263\) | |
| 6776.e4 | 6776a4 | \([0, 0, 0, 13189, 300806]\) | \(139863132/102487\) | \(-185919459539968\) | \([2]\) | \(15360\) | \(1.4263\) |
Rank
sage: E.rank()
The elliptic curves in class 6776a have rank \(0\).
Complex multiplication
The elliptic curves in class 6776a do not have complex multiplication.Modular form 6776.2.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 Cremona 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 Cremona labels.
