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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 22848.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22848.j1 | 22848cd2 | \([0, -1, 0, -3531169, -2552810687]\) | \(18575453384550358633/352517816448\) | \(92410430474944512\) | \([2]\) | \(516096\) | \(2.3791\) | |
| 22848.j2 | 22848cd1 | \([0, -1, 0, -213409, -42593471]\) | \(-4100379159705193/626805817344\) | \(-164313384181825536\) | \([2]\) | \(258048\) | \(2.0325\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22848.j have rank \(1\).
Complex multiplication
The elliptic curves in class 22848.j do not have complex multiplication.Modular form 22848.2.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.
