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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 145600.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
145600.z1 | 145600ew3 | \([0, 1, 0, -11733, -1209587]\) | \(-178643795968/524596891\) | \(-524596891000000\) | \([]\) | \(559872\) | \(1.5114\) | |
145600.z2 | 145600ew1 | \([0, 1, 0, -733, 7413]\) | \(-43614208/91\) | \(-91000000\) | \([]\) | \(62208\) | \(0.41278\) | \(\Gamma_0(N)\)-optimal |
145600.z3 | 145600ew2 | \([0, 1, 0, 1267, 38413]\) | \(224755712/753571\) | \(-753571000000\) | \([]\) | \(186624\) | \(0.96209\) |
Rank
sage: E.rank()
The elliptic curves in class 145600.z have rank \(0\).
Complex multiplication
The elliptic curves in class 145600.z do not have complex multiplication.Modular form 145600.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.