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SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 46800.ck
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46800.ck1 | 46800em2 | \([0, 0, 0, -9435, 317450]\) | \(248858189/27378\) | \(10218783744000\) | \([2]\) | \(98304\) | \(1.2297\) | |
| 46800.ck2 | 46800em1 | \([0, 0, 0, -2235, -35350]\) | \(3307949/468\) | \(174680064000\) | \([2]\) | \(49152\) | \(0.88313\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46800.ck have rank \(2\).
Complex multiplication
The elliptic curves in class 46800.ck do not have complex multiplication.Modular form 46800.2.a.ck
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.
