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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 99225j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
99225.l2 | 99225j1 | \([1, -1, 1, -230, -41478]\) | \(-9/5\) | \(-744497578125\) | \([]\) | \(95040\) | \(0.95708\) | \(\Gamma_0(N)\)-optimal |
99225.l1 | 99225j2 | \([1, -1, 1, -275855, 56075772]\) | \(-15590912409/78125\) | \(-11632774658203125\) | \([]\) | \(665280\) | \(1.9300\) |
Rank
sage: E.rank()
The elliptic curves in class 99225j have rank \(0\).
Complex multiplication
The elliptic curves in class 99225j do not have complex multiplication.Modular form 99225.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.