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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 2070.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2070.o1 | 2070p2 | \([1, -1, 1, -2183, 39777]\) | \(1577505447721/838350\) | \(611157150\) | \([2]\) | \(2304\) | \(0.63565\) | |
2070.o2 | 2070p1 | \([1, -1, 1, -113, 861]\) | \(-217081801/285660\) | \(-208246140\) | \([2]\) | \(1152\) | \(0.28908\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2070.o have rank \(0\).
Complex multiplication
The elliptic curves in class 2070.o do not have complex multiplication.Modular form 2070.2.a.o
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.