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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 28880.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28880.p1 | 28880o1 | \([0, 0, 0, -116603, -15377878]\) | \(-2520369/10\) | \(-695646742159360\) | \([]\) | \(114912\) | \(1.7053\) | \(\Gamma_0(N)\)-optimal |
28880.p2 | 28880o2 | \([0, 0, 0, -116603, 1269065898]\) | \(-2520369/10000000\) | \(-695646742159360000000\) | \([]\) | \(804384\) | \(2.6782\) |
Rank
sage: E.rank()
The elliptic curves in class 28880.p have rank \(0\).
Complex multiplication
The elliptic curves in class 28880.p do not have complex multiplication.Modular form 28880.2.a.p
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 LMFDB 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 LMFDB labels.