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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 1575.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1575.f1 | 1575e3 | \([0, 0, 1, -29550, 2045281]\) | \(-250523582464/13671875\) | \(-155731201171875\) | \([]\) | \(4320\) | \(1.4815\) | |
| 1575.f2 | 1575e1 | \([0, 0, 1, -300, -2219]\) | \(-262144/35\) | \(-398671875\) | \([]\) | \(480\) | \(0.38287\) | \(\Gamma_0(N)\)-optimal |
| 1575.f3 | 1575e2 | \([0, 0, 1, 1950, 5656]\) | \(71991296/42875\) | \(-488373046875\) | \([]\) | \(1440\) | \(0.93218\) |
Rank
sage: E.rank()
The elliptic curves in class 1575.f have rank \(0\).
Complex multiplication
The elliptic curves in class 1575.f do not have complex multiplication.Modular form 1575.2.a.f
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
