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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 30960.bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30960.bv1 | 30960ba2 | \([0, 0, 0, -28107, -1250694]\) | \(30459021867/9245000\) | \(745346396160000\) | \([2]\) | \(110592\) | \(1.5588\) | |
30960.bv2 | 30960ba1 | \([0, 0, 0, -10827, 418554]\) | \(1740992427/68800\) | \(5546763878400\) | \([2]\) | \(55296\) | \(1.2122\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30960.bv have rank \(0\).
Complex multiplication
The elliptic curves in class 30960.bv do not have complex multiplication.Modular form 30960.2.a.bv
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.