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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 33640a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33640.c2 | 33640a1 | \([0, 1, 0, -9531, -191966]\) | \(10061824/4205\) | \(40019713036880\) | \([2]\) | \(107520\) | \(1.3071\) | \(\Gamma_0(N)\)-optimal |
33640.c1 | 33640a2 | \([0, 1, 0, -131476, -18386160]\) | \(1650587344/725\) | \(110399208377600\) | \([2]\) | \(215040\) | \(1.6537\) |
Rank
sage: E.rank()
The elliptic curves in class 33640a have rank \(1\).
Complex multiplication
The elliptic curves in class 33640a do not have complex multiplication.Modular form 33640.2.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 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.