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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 162450.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162450.s1 | 162450eq4 | \([1, -1, 0, -10371417, 12858314741]\) | \(8527173507/200\) | \(2893762736634375000\) | \([2]\) | \(7962624\) | \(2.6545\) | |
162450.s2 | 162450eq3 | \([1, -1, 0, -624417, 216455741]\) | \(-1860867/320\) | \(-4630020378615000000\) | \([2]\) | \(3981312\) | \(2.3079\) | |
162450.s3 | 162450eq2 | \([1, -1, 0, -218292, -10207134]\) | \(57960603/31250\) | \(620233782714843750\) | \([2]\) | \(2654208\) | \(2.1052\) | |
162450.s4 | 162450eq1 | \([1, -1, 0, 52458, -1272384]\) | \(804357/500\) | \(-9923740523437500\) | \([2]\) | \(1327104\) | \(1.7586\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162450.s have rank \(0\).
Complex multiplication
The elliptic curves in class 162450.s do not have complex multiplication.Modular form 162450.2.a.s
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.