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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 87120.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
87120.a1 | 87120ey2 | \([0, 0, 0, -920510283, -10749550191622]\) | \(134766108430924201/283115520\) | \(181214370604729321390080\) | \([]\) | \(38320128\) | \(3.7116\) | |
87120.a2 | 87120ey1 | \([0, 0, 0, -14897883, -4821310582]\) | \(571305535801/314928000\) | \(201576654313427238912000\) | \([]\) | \(12773376\) | \(3.1623\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 87120.a have rank \(0\).
Complex multiplication
The elliptic curves in class 87120.a do not have complex multiplication.Modular form 87120.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.