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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 302016.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
302016.o1 | 302016o2 | \([0, -1, 0, -170529, 2554785]\) | \(2361864386/1355211\) | \(314682763427315712\) | \([2]\) | \(3686400\) | \(2.0472\) | |
302016.o2 | 302016o1 | \([0, -1, 0, 42431, 297409]\) | \(72765788/42471\) | \(-4930926492450816\) | \([2]\) | \(1843200\) | \(1.7006\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 302016.o have rank \(2\).
Complex multiplication
The elliptic curves in class 302016.o do not have complex multiplication.Modular form 302016.2.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.