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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 7350.cz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7350.cz1 | 7350cr2 | \([1, 0, 0, -429388, 114549392]\) | \(-7620530425/526848\) | \(-605304105000000000\) | \([]\) | \(155520\) | \(2.1630\) | |
7350.cz2 | 7350cr1 | \([1, 0, 0, 29987, 165017]\) | \(2595575/1512\) | \(-1737161015625000\) | \([]\) | \(51840\) | \(1.6137\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7350.cz have rank \(0\).
Complex multiplication
The elliptic curves in class 7350.cz do not have complex multiplication.Modular form 7350.2.a.cz
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.