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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 2300.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2300.d1 | 2300a1 | \([0, -1, 0, -1158, 68437]\) | \(-687518464/7604375\) | \(-1901093750000\) | \([]\) | \(3456\) | \(1.0381\) | \(\Gamma_0(N)\)-optimal |
2300.d2 | 2300a2 | \([0, -1, 0, 10342, -1760063]\) | \(489277573376/5615234375\) | \(-1403808593750000\) | \([]\) | \(10368\) | \(1.5874\) |
Rank
sage: E.rank()
The elliptic curves in class 2300.d have rank \(0\).
Complex multiplication
The elliptic curves in class 2300.d do not have complex multiplication.Modular form 2300.2.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.