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SageMath
E = EllipticCurve("ez1")
E.isogeny_class()
Elliptic curves in class 121680ez
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121680.dq2 | 121680ez1 | \([0, 0, 0, -1278147, -585364286]\) | \(-16022066761/998400\) | \(-14389714005943910400\) | \([2]\) | \(2580480\) | \(2.4302\) | \(\Gamma_0(N)\)-optimal |
| 121680.dq1 | 121680ez2 | \([0, 0, 0, -20746947, -36372912446]\) | \(68523370149961/243360\) | \(3507492788948828160\) | \([2]\) | \(5160960\) | \(2.7768\) |
Rank
sage: E.rank()
The elliptic curves in class 121680ez have rank \(0\).
Complex multiplication
The elliptic curves in class 121680ez do not have complex multiplication.Modular form 121680.2.a.ez
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
