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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 344760.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
344760.l1 | 344760l1 | \([0, -1, 0, -522074011, -4591198303160]\) | \(203769809659907949070336/2016474841511325\) | \(155730222612486993790800\) | \([2]\) | \(85155840\) | \(3.6102\) | \(\Gamma_0(N)\)-optimal |
344760.l2 | 344760l2 | \([0, -1, 0, -509619556, -4820669145644]\) | \(-11845731628994222232016/1269935194601506875\) | \(-1569212064440142028239840000\) | \([2]\) | \(170311680\) | \(3.9567\) |
Rank
sage: E.rank()
The elliptic curves in class 344760.l have rank \(1\).
Complex multiplication
The elliptic curves in class 344760.l do not have complex multiplication.Modular form 344760.2.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.