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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 156090.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
156090.e1 | 156090by2 | \([1, 1, 0, -20058898, 34570294708]\) | \(503835593418244309249/898614000000\) | \(1591949516454000000\) | \([2]\) | \(12902400\) | \(2.7509\) | |
156090.e2 | 156090by1 | \([1, 1, 0, -1240978, 551258932]\) | \(-119305480789133569/5200091136000\) | \(-9212278652983296000\) | \([2]\) | \(6451200\) | \(2.4044\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 156090.e have rank \(1\).
Complex multiplication
The elliptic curves in class 156090.e do not have complex multiplication.Modular form 156090.2.a.e
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.