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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 44352y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44352.ba4 | 44352y1 | \([0, 0, 0, -74856, -7882936]\) | \(62140690757632/6237\) | \(4655895552\) | \([2]\) | \(98304\) | \(1.2865\) | \(\Gamma_0(N)\)-optimal |
| 44352.ba3 | 44352y2 | \([0, 0, 0, -75036, -7843120]\) | \(3911877700432/38900169\) | \(464621128925184\) | \([2, 2]\) | \(196608\) | \(1.6330\) | |
| 44352.ba5 | 44352y3 | \([0, 0, 0, -19596, -19175056]\) | \(-17418812548/3314597517\) | \(-158357362435227648\) | \([2]\) | \(393216\) | \(1.9796\) | |
| 44352.ba2 | 44352y4 | \([0, 0, 0, -133356, 6037040]\) | \(5489767279588/2847396321\) | \(136036477698637824\) | \([2, 2]\) | \(393216\) | \(1.9796\) | |
| 44352.ba6 | 44352y5 | \([0, 0, 0, 501684, 46933616]\) | \(146142660369886/94532266521\) | \(-9032698730094133248\) | \([2]\) | \(786432\) | \(2.3262\) | |
| 44352.ba1 | 44352y6 | \([0, 0, 0, -1701516, 853470704]\) | \(5701568801608514/6277868289\) | \(599859656481964032\) | \([2]\) | \(786432\) | \(2.3262\) |
Rank
sage: E.rank()
The elliptic curves in class 44352y have rank \(0\).
Complex multiplication
The elliptic curves in class 44352y do not have complex multiplication.Modular form 44352.2.a.y
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
