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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 31824l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 31824.h2 | 31824l1 | \([0, 0, 0, -15051, 709706]\) | \(505117359652/830297\) | \(619813389312\) | \([2]\) | \(46080\) | \(1.1590\) | \(\Gamma_0(N)\)-optimal |
| 31824.h1 | 31824l2 | \([0, 0, 0, -19731, 231410]\) | \(569001644066/313788397\) | \(468483566413824\) | \([2]\) | \(92160\) | \(1.5056\) |
Rank
sage: E.rank()
The elliptic curves in class 31824l have rank \(1\).
Complex multiplication
The elliptic curves in class 31824l 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 Cremona 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 Cremona labels.
