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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1122.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1122.c1 | 1122b3 | \([1, 1, 0, -483939, 129374577]\) | \(12534210458299016895673/315581882565708\) | \(315581882565708\) | \([2]\) | \(15360\) | \(1.8903\) | |
1122.c2 | 1122b2 | \([1, 1, 0, -31399, 1848805]\) | \(3423676911662954233/483711578981136\) | \(483711578981136\) | \([2, 2]\) | \(7680\) | \(1.5437\) | |
1122.c3 | 1122b1 | \([1, 1, 0, -8279, -264363]\) | \(62768149033310713/6915442583808\) | \(6915442583808\) | \([2]\) | \(3840\) | \(1.1971\) | \(\Gamma_0(N)\)-optimal |
1122.c4 | 1122b4 | \([1, 1, 0, 51221, 10028185]\) | \(14861225463775641287/51859390496937804\) | \(-51859390496937804\) | \([2]\) | \(15360\) | \(1.8903\) |
Rank
sage: E.rank()
The elliptic curves in class 1122.c have rank \(0\).
Complex multiplication
The elliptic curves in class 1122.c do not have complex multiplication.Modular form 1122.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.