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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 84150.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84150.i1 | 84150ca1 | \([1, -1, 0, -19917, 920241]\) | \(76711450249/12622500\) | \(143778164062500\) | \([2]\) | \(368640\) | \(1.4382\) | \(\Gamma_0(N)\)-optimal |
| 84150.i2 | 84150ca2 | \([1, -1, 0, 36333, 5138991]\) | \(465664585751/1274620050\) | \(-14518719007031250\) | \([2]\) | \(737280\) | \(1.7848\) |
Rank
sage: E.rank()
The elliptic curves in class 84150.i have rank \(1\).
Complex multiplication
The elliptic curves in class 84150.i do not have complex multiplication.Modular form 84150.2.a.i
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.
