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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 47320o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47320.z1 | 47320o1 | \([0, 0, 0, -2285387, 1329795766]\) | \(267080942160036/1990625\) | \(9838967465600000\) | \([2]\) | \(752640\) | \(2.2447\) | \(\Gamma_0(N)\)-optimal |
47320.z2 | 47320o2 | \([0, 0, 0, -2238067, 1387497774]\) | \(-125415986034978/11552734375\) | \(-114202300940000000000\) | \([2]\) | \(1505280\) | \(2.5913\) |
Rank
sage: E.rank()
The elliptic curves in class 47320o have rank \(1\).
Complex multiplication
The elliptic curves in class 47320o do not have complex multiplication.Modular form 47320.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.