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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 83600be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83600.bu1 | 83600be1 | \([0, 1, 0, -10933, -518237]\) | \(-2258403328/480491\) | \(-30751424000000\) | \([]\) | \(186624\) | \(1.3095\) | \(\Gamma_0(N)\)-optimal |
83600.bu2 | 83600be2 | \([0, 1, 0, 77067, 3001763]\) | \(790939860992/517504691\) | \(-33120300224000000\) | \([]\) | \(559872\) | \(1.8588\) |
Rank
sage: E.rank()
The elliptic curves in class 83600be have rank \(0\).
Complex multiplication
The elliptic curves in class 83600be do not have complex multiplication.Modular form 83600.2.a.be
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.