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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 147294.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
147294.l1 | 147294bz4 | \([1, -1, 0, -96274278, -363558593700]\) | \(1150638118585800835537/31752757008504\) | \(2723310799674952092984\) | \([2]\) | \(24772608\) | \(3.2161\) | |
147294.l2 | 147294bz3 | \([1, -1, 0, -26878518, 48508638156]\) | \(25039399590518087377/2641281025170312\) | \(226532427999761024599752\) | \([2]\) | \(24772608\) | \(3.2161\) | |
147294.l3 | 147294bz2 | \([1, -1, 0, -6257358, -5201235180]\) | \(315922815546536017/46479778841664\) | \(3986390336187394465344\) | \([2, 2]\) | \(12386304\) | \(2.8696\) | |
147294.l4 | 147294bz1 | \([1, -1, 0, 657522, -442414764]\) | \(366554400441263/1197281046528\) | \(-102686151107527077888\) | \([2]\) | \(6193152\) | \(2.5230\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 147294.l have rank \(1\).
Complex multiplication
The elliptic curves in class 147294.l do not have complex multiplication.Modular form 147294.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.