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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 145200.ch
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
145200.ch1 | 145200dv1 | \([0, -1, 0, -1129333, 484959037]\) | \(-56197120/3267\) | \(-9260303659200000000\) | \([]\) | \(3110400\) | \(2.3956\) | \(\Gamma_0(N)\)-optimal |
145200.ch2 | 145200dv2 | \([0, -1, 0, 6130667, 855219037]\) | \(8990228480/5314683\) | \(-15064456208260800000000\) | \([]\) | \(9331200\) | \(2.9449\) |
Rank
sage: E.rank()
The elliptic curves in class 145200.ch have rank \(0\).
Complex multiplication
The elliptic curves in class 145200.ch do not have complex multiplication.Modular form 145200.2.a.ch
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.