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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 24986j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24986.i2 | 24986j1 | \([1, -1, 1, -2583, -76625]\) | \(-2146689/1664\) | \(-1476806125184\) | \([]\) | \(60480\) | \(1.0338\) | \(\Gamma_0(N)\)-optimal |
24986.i1 | 24986j2 | \([1, -1, 1, -204393, 39074515]\) | \(-1064019559329/125497034\) | \(-111379079629582154\) | \([]\) | \(423360\) | \(2.0068\) |
Rank
sage: E.rank()
The elliptic curves in class 24986j have rank \(0\).
Complex multiplication
The elliptic curves in class 24986j do not have complex multiplication.Modular form 24986.2.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.