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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 10944.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10944.l1 | 10944bi3 | \([0, 0, 0, -65676, 6478256]\) | \(1311494070536/171\) | \(4084826112\) | \([2]\) | \(24576\) | \(1.2595\) | |
| 10944.l2 | 10944bi2 | \([0, 0, 0, -4116, 100640]\) | \(2582630848/29241\) | \(87313158144\) | \([2, 2]\) | \(12288\) | \(0.91290\) | |
| 10944.l3 | 10944bi4 | \([0, 0, 0, -876, 254864]\) | \(-3112136/1172889\) | \(-28017822302208\) | \([2]\) | \(24576\) | \(1.2595\) | |
| 10944.l4 | 10944bi1 | \([0, 0, 0, -471, -1420]\) | \(247673152/124659\) | \(5816090304\) | \([2]\) | \(6144\) | \(0.56632\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10944.l have rank \(1\).
Complex multiplication
The elliptic curves in class 10944.l do not have complex multiplication.Modular form 10944.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
