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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 206400.cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 206400.cr1 | 206400en2 | \([0, -1, 0, -857633, 245587137]\) | \(34064240990978/7020421875\) | \(14377824000000000000\) | \([2]\) | \(3686400\) | \(2.3913\) | |
| 206400.cr2 | 206400en1 | \([0, -1, 0, 114367, 22999137]\) | \(161555647964/317388375\) | \(-325005696000000000\) | \([2]\) | \(1843200\) | \(2.0447\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 206400.cr have rank \(0\).
Complex multiplication
The elliptic curves in class 206400.cr do not have complex multiplication.Modular form 206400.2.a.cr
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.
