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SageMath
E = EllipticCurve("ie1")
E.isogeny_class()
Elliptic curves in class 91200ie
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91200.fx2 | 91200ie1 | \([0, 1, 0, -33, 180063]\) | \(-1/3420\) | \(-14008320000000\) | \([2]\) | \(221184\) | \(1.2014\) | \(\Gamma_0(N)\)-optimal |
| 91200.fx1 | 91200ie2 | \([0, 1, 0, -48033, 3972063]\) | \(2992209121/54150\) | \(221798400000000\) | \([2]\) | \(442368\) | \(1.5480\) |
Rank
sage: E.rank()
The elliptic curves in class 91200ie have rank \(0\).
Complex multiplication
The elliptic curves in class 91200ie do not have complex multiplication.Modular form 91200.2.a.ie
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.
