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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 1560.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1560.d1 | 1560j4 | \([0, -1, 0, -2433600, 1462052700]\) | \(1556580279686303289604/114075\) | \(116812800\) | \([4]\) | \(15360\) | \(1.9176\) | |
| 1560.d2 | 1560j5 | \([0, -1, 0, -534560, -125418900]\) | \(8248670337458940482/1446075439453125\) | \(2961562500000000000\) | \([2]\) | \(30720\) | \(2.2641\) | |
| 1560.d3 | 1560j3 | \([0, -1, 0, -155480, 21815772]\) | \(405929061432816484/35083409765625\) | \(35925411600000000\) | \([2, 2]\) | \(15360\) | \(1.9176\) | |
| 1560.d4 | 1560j2 | \([0, -1, 0, -152100, 22882500]\) | \(1520107298839022416/13013105625\) | \(3331355040000\) | \([2, 4]\) | \(7680\) | \(1.5710\) | |
| 1560.d5 | 1560j1 | \([0, -1, 0, -9295, 376432]\) | \(-5551350318708736/550618236675\) | \(-8809891786800\) | \([4]\) | \(3840\) | \(1.2244\) | \(\Gamma_0(N)\)-optimal |
| 1560.d6 | 1560j6 | \([0, -1, 0, 169520, 100725772]\) | \(263059523447441758/2294739983908125\) | \(-4699627487043840000\) | \([2]\) | \(30720\) | \(2.2641\) |
Rank
sage: E.rank()
The elliptic curves in class 1560.d have rank \(0\).
Complex multiplication
The elliptic curves in class 1560.d do not have complex multiplication.Modular form 1560.2.a.d
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
