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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 7744j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7744.bi2 | 7744j1 | \([0, -1, 0, 23071, -519583]\) | \(24167/16\) | \(-899086312013824\) | \([]\) | \(33792\) | \(1.5582\) | \(\Gamma_0(N)\)-optimal |
7744.bi1 | 7744j2 | \([0, -1, 0, -402849, -100951519]\) | \(-128667913/4096\) | \(-230166095875538944\) | \([]\) | \(101376\) | \(2.1075\) |
Rank
sage: E.rank()
The elliptic curves in class 7744j have rank \(0\).
Complex multiplication
The elliptic curves in class 7744j do not have complex multiplication.Modular form 7744.2.a.j
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.