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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 38025br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38025.h2 | 38025br1 | \([0, 0, 1, -149565, -20495264]\) | \(4206161920/371293\) | \(32662123181324325\) | \([]\) | \(423360\) | \(1.9090\) | \(\Gamma_0(N)\)-optimal |
38025.h1 | 38025br2 | \([0, 0, 1, -19329375, 32709553906]\) | \(23242854400/13\) | \(446715516533203125\) | \([]\) | \(2116800\) | \(2.7137\) |
Rank
sage: E.rank()
The elliptic curves in class 38025br have rank \(0\).
Complex multiplication
The elliptic curves in class 38025br do not have complex multiplication.Modular form 38025.2.a.br
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.