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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 2790.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2790.e1 | 2790m4 | \([1, -1, 0, -18414, -415152]\) | \(947226559343329/443751840500\) | \(323495091724500\) | \([6]\) | \(13824\) | \(1.4785\) | |
2790.e2 | 2790m2 | \([1, -1, 0, -15354, -728460]\) | \(549131937598369/307520\) | \(224182080\) | \([2]\) | \(4608\) | \(0.92922\) | |
2790.e3 | 2790m1 | \([1, -1, 0, -954, -11340]\) | \(-131794519969/3174400\) | \(-2314137600\) | \([2]\) | \(2304\) | \(0.58265\) | \(\Gamma_0(N)\)-optimal |
2790.e4 | 2790m3 | \([1, -1, 0, 4086, -50652]\) | \(10347405816671/7447750000\) | \(-5429409750000\) | \([6]\) | \(6912\) | \(1.1320\) |
Rank
sage: E.rank()
The elliptic curves in class 2790.e have rank \(0\).
Complex multiplication
The elliptic curves in class 2790.e do not have complex multiplication.Modular form 2790.2.a.e
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.