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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 29008.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29008.l1 | 29008l3 | \([0, 1, 0, -1468693, -685575101]\) | \(727057727488000/37\) | \(17829941248\) | \([]\) | \(163296\) | \(1.8882\) | |
| 29008.l2 | 29008l2 | \([0, 1, 0, -18293, -928285]\) | \(1404928000/50653\) | \(24409189568512\) | \([]\) | \(54432\) | \(1.3389\) | |
| 29008.l3 | 29008l1 | \([0, 1, 0, -2613, 50147]\) | \(4096000/37\) | \(17829941248\) | \([]\) | \(18144\) | \(0.78957\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29008.l have rank \(0\).
Complex multiplication
The elliptic curves in class 29008.l do not have complex multiplication.Modular form 29008.2.a.l
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
