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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 90480.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
90480.i1 | 90480y2 | \([0, -1, 0, -56381, 66357681]\) | \(-77426525890207744/7381623919921875\) | \(-1889695723500000000\) | \([]\) | \(1492992\) | \(2.1865\) | |
90480.i2 | 90480y1 | \([0, -1, 0, 6259, -2446095]\) | \(105908108681216/10141028512875\) | \(-2596103299296000\) | \([]\) | \(497664\) | \(1.6372\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 90480.i have rank \(0\).
Complex multiplication
The elliptic curves in class 90480.i do not have complex multiplication.Modular form 90480.2.a.i
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.