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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 2175.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2175.d1 | 2175a1 | \([0, -1, 1, -283, 1968]\) | \(-160989184/3915\) | \(-61171875\) | \([]\) | \(480\) | \(0.27955\) | \(\Gamma_0(N)\)-optimal |
| 2175.d2 | 2175a2 | \([0, -1, 1, 1217, 7593]\) | \(12747309056/9145875\) | \(-142904296875\) | \([]\) | \(1440\) | \(0.82885\) |
Rank
sage: E.rank()
The elliptic curves in class 2175.d have rank \(1\).
Complex multiplication
The elliptic curves in class 2175.d do not have complex multiplication.Modular form 2175.2.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.
