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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 250470.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
250470.o1 | 250470o2 | \([1, -1, 0, -1080855, 1121898465]\) | \(-893628963601/2960717780\) | \(-462664333552373447220\) | \([3]\) | \(9123840\) | \(2.6516\) | |
250470.o2 | 250470o1 | \([1, -1, 0, 117045, -35991675]\) | \(1134778799/4232000\) | \(-661324585821768000\) | \([]\) | \(3041280\) | \(2.1023\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 250470.o have rank \(0\).
Complex multiplication
The elliptic curves in class 250470.o do not have complex multiplication.Modular form 250470.2.a.o
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.