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SageMath
E = EllipticCurve("jx1")
E.isogeny_class()
Elliptic curves in class 158400.jx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
158400.jx1 | 158400bh1 | \([0, 0, 0, -21000, 1228750]\) | \(-56197120/3267\) | \(-59541075000000\) | \([]\) | \(414720\) | \(1.3994\) | \(\Gamma_0(N)\)-optimal |
158400.jx2 | 158400bh2 | \([0, 0, 0, 114000, 2173750]\) | \(8990228480/5314683\) | \(-96860097675000000\) | \([]\) | \(1244160\) | \(1.9487\) |
Rank
sage: E.rank()
The elliptic curves in class 158400.jx have rank \(1\).
Complex multiplication
The elliptic curves in class 158400.jx do not have complex multiplication.Modular form 158400.2.a.jx
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.