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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 4225.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4225.j1 | 4225h2 | \([0, 1, 1, -225333, -41129006]\) | \(671088640/2197\) | \(4142382567578125\) | \([]\) | \(30240\) | \(1.8621\) | |
4225.j2 | 4225h1 | \([0, 1, 1, -14083, 592869]\) | \(163840/13\) | \(24511139453125\) | \([]\) | \(10080\) | \(1.3128\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4225.j have rank \(0\).
Complex multiplication
The elliptic curves in class 4225.j do not have complex multiplication.Modular form 4225.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.