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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 428400.ct
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
428400.ct1 | 428400ct2 | \([0, 0, 0, -100875, 1480250]\) | \(2433138625/1387778\) | \(64748170368000000\) | \([2]\) | \(2654208\) | \(1.9156\) | \(\Gamma_0(N)\)-optimal* |
428400.ct2 | 428400ct1 | \([0, 0, 0, -64875, -6331750]\) | \(647214625/3332\) | \(155457792000000\) | \([2]\) | \(1327104\) | \(1.5690\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 428400.ct have rank \(1\).
Complex multiplication
The elliptic curves in class 428400.ct do not have complex multiplication.Modular form 428400.2.a.ct
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.