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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 50820q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50820.t2 | 50820q1 | \([0, 1, 0, -9960881, 16607633700]\) | \(-3856034557002072064/1973796785296875\) | \(-55947222508117074750000\) | \([2]\) | \(4838400\) | \(3.0696\) | \(\Gamma_0(N)\)-optimal |
50820.t1 | 50820q2 | \([0, 1, 0, -175352756, 893581511700]\) | \(1314817350433665559504/190690249278375\) | \(86481768627672907104000\) | \([2]\) | \(9676800\) | \(3.4161\) |
Rank
sage: E.rank()
The elliptic curves in class 50820q have rank \(1\).
Complex multiplication
The elliptic curves in class 50820q do not have complex multiplication.Modular form 50820.2.a.q
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.