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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 68952.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
68952.d1 | 68952i4 | \([0, -1, 0, -4974064, -4268164772]\) | \(2753580869496292/39328497\) | \(194387090714698752\) | \([2]\) | \(1720320\) | \(2.4568\) | |
68952.d2 | 68952i2 | \([0, -1, 0, -319804, -62575436]\) | \(2927363579728/320445801\) | \(395963053127426304\) | \([2, 2]\) | \(860160\) | \(2.1103\) | |
68952.d3 | 68952i1 | \([0, -1, 0, -75599, 6974148]\) | \(618724784128/87947613\) | \(6792101279310672\) | \([4]\) | \(430080\) | \(1.7637\) | \(\Gamma_0(N)\)-optimal |
68952.d4 | 68952i3 | \([0, -1, 0, 427176, -312066756]\) | \(1744147297148/9513325341\) | \(-47021060480887673856\) | \([2]\) | \(1720320\) | \(2.4568\) |
Rank
sage: E.rank()
The elliptic curves in class 68952.d have rank \(0\).
Complex multiplication
The elliptic curves in class 68952.d do not have complex multiplication.Modular form 68952.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.