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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 38720.ct
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38720.ct1 | 38720dd2 | \([0, 1, 0, -211185, 37297775]\) | \(-296587984/125\) | \(-439006988288000\) | \([]\) | \(152064\) | \(1.7708\) | |
38720.ct2 | 38720dd1 | \([0, 1, 0, 1775, 200143]\) | \(176/5\) | \(-17560279531520\) | \([]\) | \(50688\) | \(1.2215\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38720.ct have rank \(0\).
Complex multiplication
The elliptic curves in class 38720.ct do not have complex multiplication.Modular form 38720.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.