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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 173400.cf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
173400.cf1 | 173400eu2 | \([0, -1, 0, -4626408, -3561247188]\) | \(2885794/225\) | \(853832710778400000000\) | \([2]\) | \(9191424\) | \(2.7605\) | |
173400.cf2 | 173400eu1 | \([0, -1, 0, 286592, -249885188]\) | \(1372/15\) | \(-28461090359280000000\) | \([2]\) | \(4595712\) | \(2.4139\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 173400.cf have rank \(1\).
Complex multiplication
The elliptic curves in class 173400.cf do not have complex multiplication.Modular form 173400.2.a.cf
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.