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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 63426z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
63426.ba1 | 63426z1 | \([1, 1, 1, -1757534, -897555877]\) | \(-624757597087742358817/5477702687424\) | \(-5264072282614464\) | \([]\) | \(1814400\) | \(2.1834\) | \(\Gamma_0(N)\)-optimal |
63426.ba2 | 63426z2 | \([1, 1, 1, -903794, -1766763637]\) | \(-84958867781400698977/1353428406890670924\) | \(-1300644699021934757964\) | \([]\) | \(5443200\) | \(2.7327\) |
Rank
sage: E.rank()
The elliptic curves in class 63426z have rank \(0\).
Complex multiplication
The elliptic curves in class 63426z do not have complex multiplication.Modular form 63426.2.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 Cremona 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 Cremona labels.