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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 251280j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 251280.j1 | 251280j1 | \([0, 0, 0, -6542643, 6445459442]\) | \(-10372797669976737841/7632630000000\) | \(-22790911057920000000\) | \([]\) | \(7451136\) | \(2.6485\) | \(\Gamma_0(N)\)-optimal |
| 251280.j2 | 251280j2 | \([0, 0, 0, 26267757, -357887300398]\) | \(671282315177095816559/18919046447754148470\) | \(-56491969988250723265044480\) | \([]\) | \(52157952\) | \(3.6214\) |
Rank
sage: E.rank()
The elliptic curves in class 251280j have rank \(1\).
Complex multiplication
The elliptic curves in class 251280j do not have complex multiplication.Modular form 251280.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
