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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 63210ct
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
63210.cm2 | 63210ct1 | \([1, 0, 0, -502545, 142151337]\) | \(-119305480789133569/5200091136000\) | \(-611785522059264000\) | \([2]\) | \(1451520\) | \(2.1784\) | \(\Gamma_0(N)\)-optimal |
63210.cm1 | 63210ct2 | \([1, 0, 0, -8123025, 8910275625]\) | \(503835593418244309249/898614000000\) | \(105721038486000000\) | \([2]\) | \(2903040\) | \(2.5249\) |
Rank
sage: E.rank()
The elliptic curves in class 63210ct have rank \(1\).
Complex multiplication
The elliptic curves in class 63210ct do not have complex multiplication.Modular form 63210.2.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 Cremona 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 Cremona labels.