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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 6552.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6552.g1 | 6552c1 | \([0, 0, 0, -57966, -5371655]\) | \(49860882714802176/57967\) | \(25041744\) | \([2]\) | \(7680\) | \(1.1340\) | \(\Gamma_0(N)\)-optimal |
| 6552.g2 | 6552c2 | \([0, 0, 0, -57951, -5374574]\) | \(-3113886554501616/3360173089\) | \(-23225516391168\) | \([2]\) | \(15360\) | \(1.4806\) |
Rank
sage: E.rank()
The elliptic curves in class 6552.g have rank \(0\).
Complex multiplication
The elliptic curves in class 6552.g do not have complex multiplication.Modular form 6552.2.a.g
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.
