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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 290145w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
290145.w1 | 290145w1 | \([1, 0, 1, -33658, 2359343]\) | \(7088952961/50025\) | \(29756036633025\) | \([2]\) | \(1720320\) | \(1.4180\) | \(\Gamma_0(N)\)-optimal |
290145.w2 | 290145w2 | \([1, 0, 1, -12633, 5277613]\) | \(-374805361/20020005\) | \(-11908365860536605\) | \([2]\) | \(3440640\) | \(1.7646\) |
Rank
sage: E.rank()
The elliptic curves in class 290145w have rank \(1\).
Complex multiplication
The elliptic curves in class 290145w do not have complex multiplication.Modular form 290145.2.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.