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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 151725.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
151725.p1 | 151725bf2 | \([1, 1, 1, -29460088, -61558104844]\) | \(1526038582697/2205\) | \(4085722932435703125\) | \([2]\) | \(6684672\) | \(2.8418\) | |
151725.p2 | 151725bf1 | \([1, 1, 1, -1824463, -980814844]\) | \(-362467097/14175\) | \(-26265361708515234375\) | \([2]\) | \(3342336\) | \(2.4953\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 151725.p have rank \(1\).
Complex multiplication
The elliptic curves in class 151725.p do not have complex multiplication.Modular form 151725.2.a.p
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.