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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 270802.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270802.o1 | 270802o2 | \([1, -1, 1, -200316, 34450001]\) | \(1494447319737/5411854\) | \(3219096969047134\) | \([2]\) | \(2408448\) | \(1.8367\) | |
270802.o2 | 270802o1 | \([1, -1, 1, -6886, 1025297]\) | \(-60698457/725788\) | \(-431715628501948\) | \([2]\) | \(1204224\) | \(1.4901\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 270802.o have rank \(0\).
Complex multiplication
The elliptic curves in class 270802.o do not have complex multiplication.Modular form 270802.2.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.