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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 29040.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29040.l1 | 29040cc2 | \([0, -1, 0, -95861, -11391939]\) | \(-196566176333824/421875\) | \(-209088000000\) | \([]\) | \(93312\) | \(1.4197\) | |
29040.l2 | 29040cc1 | \([0, -1, 0, -821, -25155]\) | \(-123633664/492075\) | \(-243880243200\) | \([]\) | \(31104\) | \(0.87037\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29040.l have rank \(1\).
Complex multiplication
The elliptic curves in class 29040.l do not have complex multiplication.Modular form 29040.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.