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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 35904.cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35904.cg1 | 35904ct1 | \([0, 1, 0, -12673, -553345]\) | \(858729462625/38148\) | \(10000269312\) | \([2]\) | \(49152\) | \(0.99615\) | \(\Gamma_0(N)\)-optimal |
| 35904.cg2 | 35904ct2 | \([0, 1, 0, -12033, -611073]\) | \(-735091890625/181908738\) | \(-47686284214272\) | \([2]\) | \(98304\) | \(1.3427\) |
Rank
sage: E.rank()
The elliptic curves in class 35904.cg have rank \(0\).
Complex multiplication
The elliptic curves in class 35904.cg do not have complex multiplication.Modular form 35904.2.a.cg
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.
