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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 52416cz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 52416.cv2 | 52416cz1 | \([0, 0, 0, 411252, 1146942704]\) | \(40251338884511/2997011332224\) | \(-572737784693731098624\) | \([]\) | \(1806336\) | \(2.6626\) | \(\Gamma_0(N)\)-optimal |
| 52416.cv1 | 52416cz2 | \([0, 0, 0, -2116509708, 37478181565424]\) | \(-5486773802537974663600129/2635437714\) | \(-503639990208036864\) | \([]\) | \(12644352\) | \(3.6356\) |
Rank
sage: E.rank()
The elliptic curves in class 52416cz have rank \(0\).
Complex multiplication
The elliptic curves in class 52416cz do not have complex multiplication.Modular form 52416.2.a.cz
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
