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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 30960.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30960.a1 | 30960br1 | \([0, 0, 0, -3243, 69658]\) | \(1263214441/29025\) | \(86668185600\) | \([2]\) | \(36864\) | \(0.88511\) | \(\Gamma_0(N)\)-optimal |
30960.a2 | 30960br2 | \([0, 0, 0, 357, 215818]\) | \(1685159/6739605\) | \(-20124352696320\) | \([2]\) | \(73728\) | \(1.2317\) |
Rank
sage: E.rank()
The elliptic curves in class 30960.a have rank \(2\).
Complex multiplication
The elliptic curves in class 30960.a do not have complex multiplication.Modular form 30960.2.a.a
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.