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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 31824.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 31824.l1 | 31824x2 | \([0, 0, 0, -22071, 1262050]\) | \(6371214852688/77571\) | \(14476610304\) | \([2]\) | \(55296\) | \(1.0980\) | |
| 31824.l2 | 31824x1 | \([0, 0, 0, -1416, 18619]\) | \(26919436288/2738853\) | \(31945981392\) | \([2]\) | \(27648\) | \(0.75143\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 31824.l have rank \(1\).
Complex multiplication
The elliptic curves in class 31824.l do not have complex multiplication.Modular form 31824.2.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.
