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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 25920cv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25920.cb2 | 25920cv1 | \([0, 0, 0, -72, -234]\) | \(884736/5\) | \(233280\) | \([]\) | \(3456\) | \(-0.12806\) | \(\Gamma_0(N)\)-optimal |
25920.cb1 | 25920cv2 | \([0, 0, 0, -432, 3294]\) | \(2359296/125\) | \(472392000\) | \([]\) | \(10368\) | \(0.42124\) |
Rank
sage: E.rank()
The elliptic curves in class 25920cv have rank \(1\).
Complex multiplication
The elliptic curves in class 25920cv do not have complex multiplication.Modular form 25920.2.a.cv
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.