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SageMath
E = EllipticCurve("fj1")
E.isogeny_class()
Elliptic curves in class 158400fj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
158400.mf2 | 158400fj1 | \([0, 0, 0, 143700, -84638000]\) | \(109902239/1100000\) | \(-3284582400000000000\) | \([]\) | \(2764800\) | \(2.2341\) | \(\Gamma_0(N)\)-optimal |
158400.mf1 | 158400fj2 | \([0, 0, 0, -85536300, -304490558000]\) | \(-23178622194826561/1610510\) | \(-4808957091840000000\) | \([]\) | \(13824000\) | \(3.0388\) |
Rank
sage: E.rank()
The elliptic curves in class 158400fj have rank \(1\).
Complex multiplication
The elliptic curves in class 158400fj do not have complex multiplication.Modular form 158400.2.a.fj
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.