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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 296208e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
296208.e2 | 296208e1 | \([0, 0, 0, -161857707, -789928441830]\) | \(2393558463315519963/9284733153971\) | \(1819069321529403415498752\) | \([2]\) | \(73728000\) | \(3.5130\) | \(\Gamma_0(N)\)-optimal |
296208.e1 | 296208e2 | \([0, 0, 0, -2587307547, -50654751702390]\) | \(9776604686860471347243/147962546281\) | \(28988892218192262377472\) | \([2]\) | \(147456000\) | \(3.8596\) |
Rank
sage: E.rank()
The elliptic curves in class 296208e have rank \(0\).
Complex multiplication
The elliptic curves in class 296208e do not have complex multiplication.Modular form 296208.2.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 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.