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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 14440.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14440.g1 | 14440h3 | \([0, 0, 0, -38627, 2921934]\) | \(132304644/5\) | \(240874910720\) | \([2]\) | \(27648\) | \(1.2700\) | |
14440.g2 | 14440h2 | \([0, 0, 0, -2527, 41154]\) | \(148176/25\) | \(301093638400\) | \([2, 2]\) | \(13824\) | \(0.92343\) | |
14440.g3 | 14440h1 | \([0, 0, 0, -722, -6859]\) | \(55296/5\) | \(3763670480\) | \([2]\) | \(6912\) | \(0.57686\) | \(\Gamma_0(N)\)-optimal |
14440.g4 | 14440h4 | \([0, 0, 0, 4693, 233206]\) | \(237276/625\) | \(-30109363840000\) | \([2]\) | \(27648\) | \(1.2700\) |
Rank
sage: E.rank()
The elliptic curves in class 14440.g have rank \(0\).
Complex multiplication
The elliptic curves in class 14440.g do not have complex multiplication.Modular form 14440.2.a.g
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.