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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 1848.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1848.e1 | 1848e2 | \([0, 1, 0, -56600, -5201616]\) | \(9791533777258802/427901859\) | \(876343007232\) | \([2]\) | \(7680\) | \(1.3698\) | |
1848.e2 | 1848e1 | \([0, 1, 0, -3360, -90576]\) | \(-4097989445764/1004475087\) | \(-1028582489088\) | \([2]\) | \(3840\) | \(1.0232\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1848.e have rank \(0\).
Complex multiplication
The elliptic curves in class 1848.e do not have complex multiplication.Modular form 1848.2.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.