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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 43120.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43120.v1 | 43120bh2 | \([0, -1, 0, -4656976, -3866605504]\) | \(-23178622194826561/1610510\) | \(-776089153495040\) | \([]\) | \(792000\) | \(2.3112\) | |
43120.v2 | 43120bh1 | \([0, -1, 0, 7824, -1077824]\) | \(109902239/1100000\) | \(-530079334400000\) | \([]\) | \(158400\) | \(1.5065\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 43120.v have rank \(1\).
Complex multiplication
The elliptic curves in class 43120.v do not have complex multiplication.Modular form 43120.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.