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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 135240.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
135240.c1 | 135240do3 | \([0, -1, 0, -9088536, 10549060236]\) | \(344577854816148242/2716875\) | \(654617859840000\) | \([2]\) | \(2949120\) | \(2.4339\) | |
135240.c2 | 135240do2 | \([0, -1, 0, -568416, 164737980]\) | \(168591300897604/472410225\) | \(56912476734489600\) | \([2, 2]\) | \(1474560\) | \(2.0873\) | |
135240.c3 | 135240do4 | \([0, -1, 0, -343016, 296461740]\) | \(-18524646126002/146738831715\) | \(-35356010111873095680\) | \([2]\) | \(2949120\) | \(2.4339\) | |
135240.c4 | 135240do1 | \([0, -1, 0, -49996, 295156]\) | \(458891455696/264449745\) | \(7964735500673280\) | \([2]\) | \(737280\) | \(1.7407\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 135240.c have rank \(0\).
Complex multiplication
The elliptic curves in class 135240.c do not have complex multiplication.Modular form 135240.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.