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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2842.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2842.c1 | 2842a2 | \([1, -1, 0, -242167, -45808323]\) | \(13350003080765625/109178272\) | \(12844714522528\) | \([2]\) | \(11520\) | \(1.6860\) | |
| 2842.c2 | 2842a1 | \([1, -1, 0, -14807, -745571]\) | \(-3051779837625/295386112\) | \(-34751880690688\) | \([2]\) | \(5760\) | \(1.3395\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2842.c have rank \(0\).
Complex multiplication
The elliptic curves in class 2842.c do not have complex multiplication.Modular form 2842.2.a.c
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.
