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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 246.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
246.d1 | 246f1 | \([1, 0, 1, -2, 2]\) | \(-389017/2214\) | \(-2214\) | \([3]\) | \(20\) | \(-0.67420\) | \(\Gamma_0(N)\)-optimal |
246.d2 | 246f2 | \([1, 0, 1, 13, -58]\) | \(270840023/1654104\) | \(-1654104\) | \([]\) | \(60\) | \(-0.12490\) |
Rank
sage: E.rank()
The elliptic curves in class 246.d have rank \(0\).
Complex multiplication
The elliptic curves in class 246.d do not have complex multiplication.Modular form 246.2.a.d
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.