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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 1450.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1450.d1 | 1450c2 | \([1, 1, 0, -5950, -182250]\) | \(-2386099825/48778\) | \(-476347656250\) | \([]\) | \(3240\) | \(1.0325\) | |
1450.d2 | 1450c1 | \([1, 1, 0, 300, -1000]\) | \(304175/232\) | \(-2265625000\) | \([]\) | \(1080\) | \(0.48320\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1450.d have rank \(1\).
Complex multiplication
The elliptic curves in class 1450.d do not have complex multiplication.Modular form 1450.2.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.