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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 380880.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
380880.r1 | 380880r2 | \([0, 0, 0, -47719503, -126877402998]\) | \(16110654114672/330625\) | \(246623219725747680000\) | \([2]\) | \(24330240\) | \(3.0322\) | |
380880.r2 | 380880r1 | \([0, 0, 0, -3085128, -1838664873]\) | \(69657034752/8984375\) | \(418857370458131250000\) | \([2]\) | \(12165120\) | \(2.6857\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 380880.r have rank \(1\).
Complex multiplication
The elliptic curves in class 380880.r do not have complex multiplication.Modular form 380880.2.a.r
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.