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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 30960.ca
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30960.ca1 | 30960cb1 | \([0, 0, 0, -27507, 1618994]\) | \(770842973809/66873600\) | \(199683499622400\) | \([2]\) | \(122880\) | \(1.4847\) | \(\Gamma_0(N)\)-optimal |
30960.ca2 | 30960cb2 | \([0, 0, 0, 30093, 7505714]\) | \(1009328859791/8734528080\) | \(-26081161094430720\) | \([2]\) | \(245760\) | \(1.8313\) |
Rank
sage: E.rank()
The elliptic curves in class 30960.ca have rank \(1\).
Complex multiplication
The elliptic curves in class 30960.ca do not have complex multiplication.Modular form 30960.2.a.ca
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.