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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 95550w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95550.ck2 | 95550w1 | \([1, 1, 0, -6883125, -6973734375]\) | \(-6729249553378150807/22664098606500\) | \(-121465403469210937500\) | \([2]\) | \(6082560\) | \(2.7182\) | \(\Gamma_0(N)\)-optimal |
95550.ck1 | 95550w2 | \([1, 1, 0, -110218875, -445427321625]\) | \(27629784261491295969847/311852531250\) | \(1671334659667968750\) | \([2]\) | \(12165120\) | \(3.0648\) |
Rank
sage: E.rank()
The elliptic curves in class 95550w have rank \(0\).
Complex multiplication
The elliptic curves in class 95550w do not have complex multiplication.Modular form 95550.2.a.w
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.