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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 374790.dl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 374790.dl1 | 374790dl5 | \([1, 0, 0, -8663435, 9814118535]\) | \(81025909800741361/11088090\) | \(9840720690259290\) | \([2]\) | \(14745600\) | \(2.4811\) | |
| 374790.dl2 | 374790dl4 | \([1, 0, 0, -812065, -281511283]\) | \(66730743078481/60937500\) | \(54082255560937500\) | \([2]\) | \(7372800\) | \(2.1345\) | |
| 374790.dl3 | 374790dl3 | \([1, 0, 0, -542985, 152407125]\) | \(19948814692561/231344100\) | \(205318740327632100\) | \([2, 2]\) | \(7372800\) | \(2.1345\) | |
| 374790.dl4 | 374790dl6 | \([1, 0, 0, -110535, 388611315]\) | \(-168288035761/73415764890\) | \(-65156761583305560090\) | \([2]\) | \(14745600\) | \(2.4811\) | |
| 374790.dl5 | 374790dl2 | \([1, 0, 0, -62485, -2217775]\) | \(30400540561/15210000\) | \(13498930988010000\) | \([2, 2]\) | \(3686400\) | \(1.7879\) | |
| 374790.dl6 | 374790dl1 | \([1, 0, 0, 14395, -265023]\) | \(371694959/249600\) | \(-221520918777600\) | \([2]\) | \(1843200\) | \(1.4413\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 374790.dl have rank \(1\).
Complex multiplication
The elliptic curves in class 374790.dl do not have complex multiplication.Modular form 374790.2.a.dl
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
