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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 102675o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102675.a1 | 102675o1 | \([0, -1, 1, -11408, -476932]\) | \(-102400/3\) | \(-4810737016875\) | \([]\) | \(311040\) | \(1.2124\) | \(\Gamma_0(N)\)-optimal |
102675.a2 | 102675o2 | \([0, -1, 1, 57042, 23138318]\) | \(20480/243\) | \(-243543561479296875\) | \([]\) | \(1555200\) | \(2.0171\) |
Rank
sage: E.rank()
The elliptic curves in class 102675o have rank \(2\).
Complex multiplication
The elliptic curves in class 102675o do not have complex multiplication.Modular form 102675.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.