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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 48400.ci
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48400.ci1 | 48400bx4 | \([0, 1, 0, -6075208, -5765686412]\) | \(-349938025/8\) | \(-566899520000000000\) | \([]\) | \(972000\) | \(2.5200\) | |
48400.ci2 | 48400bx3 | \([0, 1, 0, -25208, -18186412]\) | \(-25/2\) | \(-141724880000000000\) | \([]\) | \(324000\) | \(1.9707\) | |
48400.ci3 | 48400bx1 | \([0, 1, 0, -5848, 205588]\) | \(-121945/32\) | \(-5805051084800\) | \([]\) | \(64800\) | \(1.1660\) | \(\Gamma_0(N)\)-optimal |
48400.ci4 | 48400bx2 | \([0, 1, 0, 42552, -1517452]\) | \(46969655/32768\) | \(-5944372310835200\) | \([]\) | \(194400\) | \(1.7153\) |
Rank
sage: E.rank()
The elliptic curves in class 48400.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 48400.ci do not have complex multiplication.Modular form 48400.2.a.ci
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 15 & 5 \\ 3 & 1 & 5 & 15 \\ 15 & 5 & 1 & 3 \\ 5 & 15 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.