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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 439569bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 439569.bg1 | 439569bg1 | \([1, -1, 1, -284824013, 1850082928724]\) | \(147815204204011553/15178486401\) | \(262399420848440508612993\) | \([2]\) | \(107347968\) | \(3.5266\) | \(\Gamma_0(N)\)-optimal |
| 439569.bg2 | 439569bg2 | \([1, -1, 1, -262974848, 2145833226164]\) | \(-116340772335201233/47730591665289\) | \(-825146808373467883655607177\) | \([2]\) | \(214695936\) | \(3.8731\) |
Rank
sage: E.rank()
The elliptic curves in class 439569bg have rank \(0\).
Complex multiplication
The elliptic curves in class 439569bg do not have complex multiplication.Modular form 439569.2.a.bg
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
