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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 145600di
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
145600.hm2 | 145600di1 | \([0, -1, 0, -733, -7413]\) | \(-43614208/91\) | \(-91000000\) | \([]\) | \(62208\) | \(0.41278\) | \(\Gamma_0(N)\)-optimal |
145600.hm3 | 145600di2 | \([0, -1, 0, 1267, -38413]\) | \(224755712/753571\) | \(-753571000000\) | \([]\) | \(186624\) | \(0.96209\) | |
145600.hm1 | 145600di3 | \([0, -1, 0, -11733, 1209587]\) | \(-178643795968/524596891\) | \(-524596891000000\) | \([]\) | \(559872\) | \(1.5114\) |
Rank
sage: E.rank()
The elliptic curves in class 145600di have rank \(0\).
Complex multiplication
The elliptic curves in class 145600di do not have complex multiplication.Modular form 145600.2.a.di
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.