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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 127296cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
127296.dh2 | 127296cb1 | \([0, 0, 0, 456, 920]\) | \(14047232/8619\) | \(-6434049024\) | \([2]\) | \(65536\) | \(0.57124\) | \(\Gamma_0(N)\)-optimal |
127296.dh1 | 127296cb2 | \([0, 0, 0, -1884, 7472]\) | \(61918288/33813\) | \(403860307968\) | \([2]\) | \(131072\) | \(0.91781\) |
Rank
sage: E.rank()
The elliptic curves in class 127296cb have rank \(1\).
Complex multiplication
The elliptic curves in class 127296cb do not have complex multiplication.Modular form 127296.2.a.cb
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.