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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 440818c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
440818.c2 | 440818c1 | \([1, 0, 1, -806, -82824]\) | \(-42223146625/2136719872\) | \(-2925169504768\) | \([]\) | \(878688\) | \(1.0720\) | \(\Gamma_0(N)\)-optimal |
440818.c1 | 440818c2 | \([1, 0, 1, -171006, -27233128]\) | \(-403971436666266625/7425063688\) | \(-10164912188872\) | \([]\) | \(2636064\) | \(1.6213\) |
Rank
sage: E.rank()
The elliptic curves in class 440818c have rank \(0\).
Complex multiplication
The elliptic curves in class 440818c do not have complex multiplication.Modular form 440818.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.