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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 301530cj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
301530.cj3 | 301530cj1 | \([1, 1, 1, -16410, -811113]\) | \(3301293169/22800\) | \(3375218269200\) | \([2]\) | \(788480\) | \(1.2375\) | \(\Gamma_0(N)\)-optimal |
301530.cj2 | 301530cj2 | \([1, 1, 1, -26990, 348455]\) | \(14688124849/8122500\) | \(1202421508402500\) | \([2, 2]\) | \(1576960\) | \(1.5841\) | |
301530.cj1 | 301530cj3 | \([1, 1, 1, -328520, 72233207]\) | \(26487576322129/44531250\) | \(6592223182031250\) | \([2]\) | \(3153920\) | \(1.9307\) | |
301530.cj4 | 301530cj4 | \([1, 1, 1, 105260, 2887655]\) | \(871257511151/527800050\) | \(-78133349615994450\) | \([2]\) | \(3153920\) | \(1.9307\) |
Rank
sage: E.rank()
The elliptic curves in class 301530cj have rank \(1\).
Complex multiplication
The elliptic curves in class 301530cj do not have complex multiplication.Modular form 301530.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.