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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 253920.ct
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
253920.ct1 | 253920ct4 | \([0, 1, 0, -43025, -3446337]\) | \(14526784/15\) | \(9095325020160\) | \([2]\) | \(788480\) | \(1.4045\) | |
253920.ct2 | 253920ct2 | \([0, 1, 0, -29800, 1952108]\) | \(38614472/405\) | \(30696721943040\) | \([2]\) | \(788480\) | \(1.4045\) | |
253920.ct3 | 253920ct1 | \([0, 1, 0, -3350, -26352]\) | \(438976/225\) | \(2131716801600\) | \([2, 2]\) | \(394240\) | \(1.0579\) | \(\Gamma_0(N)\)-optimal |
253920.ct4 | 253920ct3 | \([0, 1, 0, 12520, -191400]\) | \(2863288/1875\) | \(-142114453440000\) | \([2]\) | \(788480\) | \(1.4045\) |
Rank
sage: E.rank()
The elliptic curves in class 253920.ct have rank \(0\).
Complex multiplication
The elliptic curves in class 253920.ct do not have complex multiplication.Modular form 253920.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.