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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 439569.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 439569.j1 | 439569j1 | \([1, -1, 1, -82314139667, 9089128172263650]\) | \(147815204204011553/15178486401\) | \(6333684126289271319041212834017\) | \([2]\) | \(1824915456\) | \(4.9432\) | \(\Gamma_0(N)\)-optimal |
| 439569.j2 | 439569j2 | \([1, -1, 1, -75999730982, 10542174641221110]\) | \(-116340772335201233/47730591665289\) | \(-19917038022244358811021190471732713\) | \([2]\) | \(3649830912\) | \(5.2897\) |
Rank
sage: E.rank()
The elliptic curves in class 439569.j have rank \(0\).
Complex multiplication
The elliptic curves in class 439569.j do not have complex multiplication.Modular form 439569.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
