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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 3528.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3528.t1 | 3528p1 | \([0, 0, 0, -294, -1715]\) | \(55296/7\) | \(355770576\) | \([2]\) | \(1536\) | \(0.37003\) | \(\Gamma_0(N)\)-optimal |
3528.t2 | 3528p2 | \([0, 0, 0, 441, -8918]\) | \(11664/49\) | \(-39846304512\) | \([2]\) | \(3072\) | \(0.71661\) |
Rank
sage: E.rank()
The elliptic curves in class 3528.t have rank \(1\).
Complex multiplication
The elliptic curves in class 3528.t do not have complex multiplication.Modular form 3528.2.a.t
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.