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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 310464cj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.cj2 | 310464cj1 | \([0, 0, 0, -409836, 104420176]\) | \(-338608873/13552\) | \(-304690619165442048\) | \([2]\) | \(3538944\) | \(2.1231\) | \(\Gamma_0(N)\)-optimal |
310464.cj1 | 310464cj2 | \([0, 0, 0, -6619116, 6554620240]\) | \(1426487591593/2156\) | \(48473507594502144\) | \([2]\) | \(7077888\) | \(2.4697\) |
Rank
sage: E.rank()
The elliptic curves in class 310464cj have rank \(2\).
Complex multiplication
The elliptic curves in class 310464cj do not have complex multiplication.Modular form 310464.2.a.cj
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.