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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 317400.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 317400.l1 | 317400l2 | \([0, -1, 0, -1576741808, -24097917356388]\) | \(15043017316604/243\) | \(7002881547768144000000\) | \([2]\) | \(135659520\) | \(3.7371\) | |
| 317400.l2 | 317400l1 | \([0, -1, 0, -98451308, -377267993388]\) | \(-14647977776/59049\) | \(-425425054026914748000000\) | \([2]\) | \(67829760\) | \(3.3905\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 317400.l have rank \(0\).
Complex multiplication
The elliptic curves in class 317400.l do not have complex multiplication.Modular form 317400.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
