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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 254016.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254016.z1 | 254016z1 | \([0, 0, 0, -19404, -1136016]\) | \(-35937/4\) | \(-89932296093696\) | \([]\) | \(663552\) | \(1.4149\) | \(\Gamma_0(N)\)-optimal |
254016.z2 | 254016z2 | \([0, 0, 0, 121716, 1629936]\) | \(109503/64\) | \(-116552255737430016\) | \([]\) | \(1990656\) | \(1.9642\) |
Rank
sage: E.rank()
The elliptic curves in class 254016.z have rank \(2\).
Complex multiplication
The elliptic curves in class 254016.z do not have complex multiplication.Modular form 254016.2.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.