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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 4950.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4950.e1 | 4950i1 | \([1, -1, 0, -5202, -146124]\) | \(-854307420745/20785248\) | \(-378811144800\) | \([]\) | \(9600\) | \(1.0071\) | \(\Gamma_0(N)\)-optimal |
4950.e2 | 4950i2 | \([1, -1, 0, 28008, 6665166]\) | \(341297975/2898918\) | \(-20637804902343750\) | \([]\) | \(48000\) | \(1.8118\) |
Rank
sage: E.rank()
The elliptic curves in class 4950.e have rank \(0\).
Complex multiplication
The elliptic curves in class 4950.e do not have complex multiplication.Modular form 4950.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.