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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 226941.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
226941.e1 | 226941h2 | \([1, 1, 1, -6888, -168378]\) | \(244140625/61347\) | \(9081557682483\) | \([2]\) | \(405504\) | \(1.1964\) | |
226941.e2 | 226941h1 | \([1, 1, 1, 1047, -16026]\) | \(857375/1287\) | \(-190522189143\) | \([2]\) | \(202752\) | \(0.84981\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 226941.e have rank \(1\).
Complex multiplication
The elliptic curves in class 226941.e do not have complex multiplication.Modular form 226941.2.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.