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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 39270t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39270.q2 | 39270t1 | \([1, 1, 0, 588, 204624]\) | \(22423382364599/18057977118720\) | \(-18057977118720\) | \([2]\) | \(125440\) | \(1.2227\) | \(\Gamma_0(N)\)-optimal |
39270.q1 | 39270t2 | \([1, 1, 0, -48692, 4018896]\) | \(12767635874606888521/340593309302400\) | \(340593309302400\) | \([2]\) | \(250880\) | \(1.5693\) |
Rank
sage: E.rank()
The elliptic curves in class 39270t have rank \(0\).
Complex multiplication
The elliptic curves in class 39270t do not have complex multiplication.Modular form 39270.2.a.t
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.