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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 23184.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23184.z1 | 23184bg1 | \([0, 0, 0, -4306440, 3439817516]\) | \(-47327266415721472000/1222082060283\) | \(-228069842418254592\) | \([]\) | \(380160\) | \(2.4375\) | \(\Gamma_0(N)\)-optimal |
23184.z2 | 23184bg2 | \([0, 0, 0, -1332120, 8074892828]\) | \(-1400832679220224000/150124273180279587\) | \(-28016792357996497644288\) | \([]\) | \(1140480\) | \(2.9868\) |
Rank
sage: E.rank()
The elliptic curves in class 23184.z have rank \(1\).
Complex multiplication
The elliptic curves in class 23184.z do not have complex multiplication.Modular form 23184.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.