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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 188496.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 188496.n1 | 188496l4 | \([0, 0, 0, -52193091, -103080836990]\) | \(5265932508006615127873/1510137598013239041\) | \(4509246705465963564601344\) | \([2]\) | \(23592960\) | \(3.4372\) | |
| 188496.n2 | 188496l2 | \([0, 0, 0, -19475571, 31813497970]\) | \(273594167224805799793/11903648120953281\) | \(35544102830796561813504\) | \([2, 2]\) | \(11796480\) | \(3.0906\) | |
| 188496.n3 | 188496l1 | \([0, 0, 0, -19267491, 32552556514]\) | \(264918160154242157473/536027170833\) | \(1600568555672604672\) | \([2]\) | \(5898240\) | \(2.7440\) | \(\Gamma_0(N)\)-optimal |
| 188496.n4 | 188496l3 | \([0, 0, 0, 9912669, 119408086114]\) | \(36075142039228937567/2083708275110728497\) | \(-6221919570148233520386048\) | \([2]\) | \(23592960\) | \(3.4372\) |
Rank
sage: E.rank()
The elliptic curves in class 188496.n have rank \(1\).
Complex multiplication
The elliptic curves in class 188496.n do not have complex multiplication.Modular form 188496.2.a.n
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.
