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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 89280bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 89280.g3 | 89280bv1 | \([0, 0, 0, -61068, -5928208]\) | \(-131794519969/3174400\) | \(-606637287014400\) | \([2]\) | \(442368\) | \(1.6224\) | \(\Gamma_0(N)\)-optimal |
| 89280.g2 | 89280bv2 | \([0, 0, 0, -982668, -374936848]\) | \(549131937598369/307520\) | \(58767987179520\) | \([2]\) | \(884736\) | \(1.9689\) | |
| 89280.g4 | 89280bv3 | \([0, 0, 0, 261492, -25410832]\) | \(10347405816671/7447750000\) | \(-1423287189504000000\) | \([2]\) | \(1327104\) | \(2.1717\) | |
| 89280.g1 | 89280bv4 | \([0, 0, 0, -1178508, -214914832]\) | \(947226559343329/443751840500\) | \(84802297325027328000\) | \([2]\) | \(2654208\) | \(2.5182\) |
Rank
sage: E.rank()
The elliptic curves in class 89280bv have rank \(1\).
Complex multiplication
The elliptic curves in class 89280bv do not have complex multiplication.Modular form 89280.2.a.bv
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
