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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 18876.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18876.k1 | 18876h4 | \([0, 1, 0, -90548, 9705540]\) | \(181037698000/14480427\) | \(6567157692556032\) | \([2]\) | \(103680\) | \(1.7784\) | |
| 18876.k2 | 18876h3 | \([0, 1, 0, -88733, 10144044]\) | \(2725888000000/19773\) | \(560465210448\) | \([2]\) | \(51840\) | \(1.4318\) | |
| 18876.k3 | 18876h2 | \([0, 1, 0, -17948, -928908]\) | \(1409938000/4563\) | \(2069410007808\) | \([2]\) | \(34560\) | \(1.2291\) | |
| 18876.k4 | 18876h1 | \([0, 1, 0, -1613, -1080]\) | \(16384000/9477\) | \(268625337552\) | \([2]\) | \(17280\) | \(0.88253\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18876.k have rank \(0\).
Complex multiplication
The elliptic curves in class 18876.k do not have complex multiplication.Modular form 18876.2.a.k
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
