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SageMath
E = EllipticCurve("ey1")
E.isogeny_class()
Elliptic curves in class 333200.ey
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 333200.ey1 | 333200ey1 | \([0, 1, 0, -21968, -1260652]\) | \(-4768951705/272\) | \(-66874572800\) | \([]\) | \(331776\) | \(1.1411\) | \(\Gamma_0(N)\)-optimal |
| 333200.ey2 | 333200ey2 | \([0, 1, 0, -2368, -3385292]\) | \(-5975305/20123648\) | \(-4947648394035200\) | \([]\) | \(995328\) | \(1.6904\) |
Rank
sage: E.rank()
The elliptic curves in class 333200.ey have rank \(1\).
Complex multiplication
The elliptic curves in class 333200.ey do not have complex multiplication.Modular form 333200.2.a.ey
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.
