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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 87362.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
87362.r1 | 87362t2 | \([1, 1, 0, -18779, -1025251]\) | \(-128667913/4096\) | \(-23316691357696\) | \([]\) | \(342144\) | \(1.3410\) | |
87362.r2 | 87362t1 | \([1, 1, 0, 1076, -4704]\) | \(24167/16\) | \(-91080825616\) | \([]\) | \(114048\) | \(0.79171\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 87362.r have rank \(1\).
Complex multiplication
The elliptic curves in class 87362.r do not have complex multiplication.Modular form 87362.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.