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SageMath
E = EllipticCurve("jj1")
E.isogeny_class()
Elliptic curves in class 193600jj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193600.im2 | 193600jj1 | \([0, -1, 0, -4033, -384063]\) | \(-121\) | \(-59969536000000\) | \([]\) | \(430080\) | \(1.3265\) | \(\Gamma_0(N)\)-optimal |
193600.im1 | 193600jj2 | \([0, -1, 0, -5812033, 5395247937]\) | \(-24729001\) | \(-878013976576000000\) | \([]\) | \(4730880\) | \(2.5254\) |
Rank
sage: E.rank()
The elliptic curves in class 193600jj have rank \(0\).
Complex multiplication
The elliptic curves in class 193600jj do not have complex multiplication.Modular form 193600.2.a.jj
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.
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.