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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 299538j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
299538.j1 | 299538j1 | \([1, -1, 0, -358128, -337087232]\) | \(-9920726433/90177536\) | \(-46173640457541648384\) | \([]\) | \(8382528\) | \(2.4557\) | \(\Gamma_0(N)\)-optimal |
299538.j2 | 299538j2 | \([1, -1, 0, 3191952, 8620237952]\) | \(1070599167/10176896\) | \(-34188584995881955937664\) | \([]\) | \(25147584\) | \(3.0050\) |
Rank
sage: E.rank()
The elliptic curves in class 299538j have rank \(0\).
Complex multiplication
The elliptic curves in class 299538j do not have complex multiplication.Modular form 299538.2.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.