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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 29624o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29624.c2 | 29624o1 | \([0, 1, 0, -84, -224]\) | \(21296/7\) | \(21803264\) | \([2]\) | \(5376\) | \(0.11112\) | \(\Gamma_0(N)\)-optimal |
29624.c1 | 29624o2 | \([0, 1, 0, -544, 4560]\) | \(1431644/49\) | \(610491392\) | \([2]\) | \(10752\) | \(0.45770\) |
Rank
sage: E.rank()
The elliptic curves in class 29624o have rank \(2\).
Complex multiplication
The elliptic curves in class 29624o do not have complex multiplication.Modular form 29624.2.a.o
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.