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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 4680.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4680.r1 | 4680c2 | \([0, 0, 0, -627, -6034]\) | \(492983766/845\) | \(46725120\) | \([2]\) | \(1536\) | \(0.36604\) | |
| 4680.r2 | 4680c1 | \([0, 0, 0, -27, -154]\) | \(-78732/325\) | \(-8985600\) | \([2]\) | \(768\) | \(0.019466\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4680.r have rank \(1\).
Complex multiplication
The elliptic curves in class 4680.r do not have complex multiplication.Modular form 4680.2.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.
