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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 360789.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
360789.j1 | 360789j2 | \([0, 1, 1, -425515660683913, -3378480795322981367837]\) | \(-17032812843524919638015362135588864000/45445783003836939867\) | \(-22734089931873408868213806416187\) | \([]\) | \(44487429120\) | \(6.6197\) | |
360789.j2 | 360789j1 | \([0, 1, 1, -5251531101343, -4637645406687259238]\) | \(-32018247290363937163403702272000/44454409555957421205645603\) | \(-22238158920666900766172008822951860483\) | \([3]\) | \(14829143040\) | \(6.0704\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 360789.j have rank \(0\).
Complex multiplication
The elliptic curves in class 360789.j do not have complex multiplication.Modular form 360789.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.