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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 35490.ct
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35490.ct1 | 35490cu4 | \([1, 1, 1, -22966005, -42371553645]\) | \(277536408914951281369/2063880\) | \(9961954558920\) | \([2]\) | \(1548288\) | \(2.5451\) | |
35490.ct2 | 35490cu3 | \([1, 1, 1, -1536805, -563630605]\) | \(83161039719198169/19757817763320\) | \(95367212600352845880\) | \([2]\) | \(1548288\) | \(2.5451\) | |
35490.ct3 | 35490cu2 | \([1, 1, 1, -1435405, -662475325]\) | \(67762119444423769/5843073600\) | \(28203400240142400\) | \([2, 2]\) | \(774144\) | \(2.1986\) | |
35490.ct4 | 35490cu1 | \([1, 1, 1, -83405, -11892925]\) | \(-13293525831769/4892160000\) | \(-23613521917440000\) | \([4]\) | \(387072\) | \(1.8520\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35490.ct have rank \(0\).
Complex multiplication
The elliptic curves in class 35490.ct do not have complex multiplication.Modular form 35490.2.a.ct
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.