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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 1950o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1950.t2 | 1950o1 | \([1, 1, 1, 12, -339]\) | \(7604375/2047032\) | \(-51175800\) | \([]\) | \(648\) | \(0.15840\) | \(\Gamma_0(N)\)-optimal |
1950.t1 | 1950o2 | \([1, 1, 1, -3363, -76479]\) | \(-168256703745625/30371328\) | \(-759283200\) | \([]\) | \(1944\) | \(0.70771\) |
Rank
sage: E.rank()
The elliptic curves in class 1950o have rank \(0\).
Complex multiplication
The elliptic curves in class 1950o do not have complex multiplication.Modular form 1950.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.