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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 20070.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20070.be1 | 20070bg3 | \([1, -1, 1, -757697342, -7799122947891]\) | \(65990812340278189764070806169/2142150634958771454912000\) | \(1561627812884944390630848000\) | \([2]\) | \(11073024\) | \(3.9917\) | |
| 20070.be2 | 20070bg2 | \([1, -1, 1, -115457342, 308001020109]\) | \(233486000400975208694166169/78913673205682176000000\) | \(57528067766942306304000000\) | \([2, 2]\) | \(5536512\) | \(3.6452\) | |
| 20070.be3 | 20070bg1 | \([1, -1, 1, -103660862, 406176045261]\) | \(168982070711351853939176089/37703877214076928000\) | \(27486126489062080512000\) | \([4]\) | \(2768256\) | \(3.2986\) | \(\Gamma_0(N)\)-optimal |
| 20070.be4 | 20070bg4 | \([1, -1, 1, 338038978, 2131781820621]\) | \(5859985279907178462243106151/6084442029900375000000000\) | \(-4435558239797373375000000000\) | \([2]\) | \(11073024\) | \(3.9917\) |
Rank
sage: E.rank()
The elliptic curves in class 20070.be have rank \(0\).
Complex multiplication
The elliptic curves in class 20070.be do not have complex multiplication.Modular form 20070.2.a.be
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.
