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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 209484h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
209484.m2 | 209484h1 | \([0, 0, 0, 836272824, 1292355805205]\) | \(37458737578627432448/22095372689637291\) | \(-38151872532092012302032857136\) | \([2]\) | \(133816320\) | \(4.1737\) | \(\Gamma_0(N)\)-optimal |
209484.m1 | 209484h2 | \([0, 0, 0, -3380711511, 10390077809534]\) | \(154672654658139268432/87821582162841747\) | \(2426251219425535065892081281792\) | \([2]\) | \(267632640\) | \(4.5202\) |
Rank
sage: E.rank()
The elliptic curves in class 209484h have rank \(0\).
Complex multiplication
The elliptic curves in class 209484h do not have complex multiplication.Modular form 209484.2.a.h
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.