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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 248430.dm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
248430.dm1 | 248430dm2 | \([1, 0, 1, -6550444, 50910161642]\) | \(-131425499875625809/4658135040000000\) | \(-1101712478580080640000000\) | \([]\) | \(33191424\) | \(3.2935\) | |
248430.dm2 | 248430dm1 | \([1, 0, 1, -1167794, -490055044]\) | \(-744673162316209/7529822040\) | \(-1780905626762447640\) | \([]\) | \(4741632\) | \(2.3205\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 248430.dm have rank \(1\).
Complex multiplication
The elliptic curves in class 248430.dm do not have complex multiplication.Modular form 248430.2.a.dm
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.