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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 244881z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
244881.z1 | 244881z1 | \([0, 0, 1, -66448434, -208485206433]\) | \(-9221261135586623488/121324931\) | \(-426911344010005491\) | \([]\) | \(17418240\) | \(2.9413\) | \(\Gamma_0(N)\)-optimal |
244881.z2 | 244881z2 | \([0, 0, 1, -62691564, -233098419330]\) | \(-7743965038771437568/2189290237869371\) | \(-7703551365521055139244331\) | \([]\) | \(52254720\) | \(3.4906\) |
Rank
sage: E.rank()
The elliptic curves in class 244881z have rank \(1\).
Complex multiplication
The elliptic curves in class 244881z do not have complex multiplication.Modular form 244881.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.