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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 3528.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3528.m1 | 3528i2 | \([0, 0, 0, -1155, -13426]\) | \(665500/81\) | \(20739898368\) | \([2]\) | \(2048\) | \(0.71000\) | |
| 3528.m2 | 3528i1 | \([0, 0, 0, 105, -1078]\) | \(2000/9\) | \(-576108288\) | \([2]\) | \(1024\) | \(0.36342\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3528.m have rank \(1\).
Complex multiplication
The elliptic curves in class 3528.m do not have complex multiplication.Modular form 3528.2.a.m
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.
