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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 12342.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12342.l1 | 12342o1 | \([1, 0, 1, -23961, -1429496]\) | \(858729462625/38148\) | \(67581509028\) | \([2]\) | \(30720\) | \(1.1554\) | \(\Gamma_0(N)\)-optimal |
12342.l2 | 12342o2 | \([1, 0, 1, -22751, -1580020]\) | \(-735091890625/181908738\) | \(-322262425800018\) | \([2]\) | \(61440\) | \(1.5019\) |
Rank
sage: E.rank()
The elliptic curves in class 12342.l have rank \(0\).
Complex multiplication
The elliptic curves in class 12342.l do not have complex multiplication.Modular form 12342.2.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.