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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 59150.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59150.e1 | 59150ba2 | \([1, 0, 1, -126416, 17289378]\) | \(370300910741/4732\) | \(2855057523500\) | \([2]\) | \(258048\) | \(1.5357\) | |
59150.e2 | 59150ba1 | \([1, 0, 1, -8116, 254178]\) | \(97972181/10192\) | \(6149354666000\) | \([2]\) | \(129024\) | \(1.1891\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 59150.e have rank \(1\).
Complex multiplication
The elliptic curves in class 59150.e do not have complex multiplication.Modular form 59150.2.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.