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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 44400.dg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44400.dg1 | 44400cv4 | \([0, 1, 0, -128183408, 114956575188]\) | \(3639478711331685826729/2016912141902025000\) | \(129082377081729600000000000\) | \([4]\) | \(13271040\) | \(3.7007\) | |
44400.dg2 | 44400cv2 | \([0, 1, 0, -78183408, -264543424812]\) | \(825824067562227826729/5613755625000000\) | \(359280360000000000000000\) | \([2, 2]\) | \(6635520\) | \(3.3541\) | |
44400.dg3 | 44400cv1 | \([0, 1, 0, -78055408, -265457600812]\) | \(821774646379511057449/38361600000\) | \(2455142400000000000\) | \([2]\) | \(3317760\) | \(3.0075\) | \(\Gamma_0(N)\)-optimal |
44400.dg4 | 44400cv3 | \([0, 1, 0, -30231408, -585534112812]\) | \(-47744008200656797609/2286529541015625000\) | \(-146337890625000000000000000\) | \([2]\) | \(13271040\) | \(3.7007\) |
Rank
sage: E.rank()
The elliptic curves in class 44400.dg have rank \(0\).
Complex multiplication
The elliptic curves in class 44400.dg do not have complex multiplication.Modular form 44400.2.a.dg
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.