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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 17472.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17472.y1 | 17472m2 | \([0, -1, 0, -235167745, -1388002409471]\) | \(-5486773802537974663600129/2635437714\) | \(-690864184098816\) | \([]\) | \(1580544\) | \(3.0863\) | |
17472.y2 | 17472m1 | \([0, -1, 0, 45695, -42494591]\) | \(40251338884511/2997011332224\) | \(-785648538674528256\) | \([]\) | \(225792\) | \(2.1133\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17472.y have rank \(1\).
Complex multiplication
The elliptic curves in class 17472.y do not have complex multiplication.Modular form 17472.2.a.y
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.