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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 64400.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64400.l1 | 64400bu2 | \([0, 1, 0, -2528, 111988]\) | \(-17455277065/43606528\) | \(-4465308467200\) | \([]\) | \(124416\) | \(1.1152\) | |
| 64400.l2 | 64400bu1 | \([0, 1, 0, 272, -3372]\) | \(21653735/63112\) | \(-6462668800\) | \([]\) | \(41472\) | \(0.56587\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 64400.l have rank \(1\).
Complex multiplication
The elliptic curves in class 64400.l do not have complex multiplication.Modular form 64400.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
