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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 236691.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
236691.l1 | 236691l3 | \([0, 0, 1, -305184, 159934117]\) | \(-178643795968/524596891\) | \(-9230957873545826691\) | \([]\) | \(3981312\) | \(2.3260\) | |
236691.l2 | 236691l1 | \([0, 0, 1, -19074, -1015763]\) | \(-43614208/91\) | \(-1601262189891\) | \([]\) | \(442368\) | \(1.2274\) | \(\Gamma_0(N)\)-optimal |
236691.l3 | 236691l2 | \([0, 0, 1, 32946, -5039510]\) | \(224755712/753571\) | \(-13260052194487371\) | \([]\) | \(1327104\) | \(1.7767\) |
Rank
sage: E.rank()
The elliptic curves in class 236691.l have rank \(1\).
Complex multiplication
The elliptic curves in class 236691.l do not have complex multiplication.Modular form 236691.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.