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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 30576.cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30576.cr1 | 30576cu2 | \([0, 1, 0, -2880804880, -59514924513388]\) | \(-5486773802537974663600129/2635437714\) | \(-1269991881172525056\) | \([]\) | \(9483264\) | \(3.7127\) | |
| 30576.cr2 | 30576cu1 | \([0, 1, 0, 559760, -1821115948]\) | \(40251338884511/2997011332224\) | \(-1444230701976868356096\) | \([]\) | \(1354752\) | \(2.7397\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30576.cr have rank \(1\).
Complex multiplication
The elliptic curves in class 30576.cr do not have complex multiplication.Modular form 30576.2.a.cr
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.
