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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 1584.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1584.l1 | 1584a2 | \([0, 0, 0, -75, 234]\) | \(1687500/121\) | \(3345408\) | \([2]\) | \(256\) | \(-0.0012397\) | |
1584.l2 | 1584a1 | \([0, 0, 0, -15, -18]\) | \(54000/11\) | \(76032\) | \([2]\) | \(128\) | \(-0.34781\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1584.l have rank \(1\).
Complex multiplication
The elliptic curves in class 1584.l do not have complex multiplication.Modular form 1584.2.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.