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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 4620.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4620.e1 | 4620e2 | \([0, -1, 0, -98619500, -375994125000]\) | \(414354576760345737269208016/1182266314178222109375\) | \(302660176429624860000000\) | \([2]\) | \(873600\) | \(3.3770\) | |
4620.e2 | 4620e1 | \([0, -1, 0, -3697625, -10620843750]\) | \(-349439858058052607328256/2844147488104248046875\) | \(-45506359809667968750000\) | \([2]\) | \(436800\) | \(3.0305\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4620.e have rank \(0\).
Complex multiplication
The elliptic curves in class 4620.e do not have complex multiplication.Modular form 4620.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.