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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 376768l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 376768.l2 | 376768l1 | \([0, 1, 0, -512449, -148701633]\) | \(-95443993/5887\) | \(-917956169754738688\) | \([2]\) | \(5160960\) | \(2.2012\) | \(\Gamma_0(N)\)-optimal |
| 376768.l1 | 376768l2 | \([0, 1, 0, -8316929, -9234677249]\) | \(408023180713/1421\) | \(221575627182178304\) | \([2]\) | \(10321920\) | \(2.5477\) |
Rank
sage: E.rank()
The elliptic curves in class 376768l have rank \(0\).
Complex multiplication
The elliptic curves in class 376768l do not have complex multiplication.Modular form 376768.2.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.
