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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 14440.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14440.l1 | 14440j1 | \([0, -1, 0, -12755, -474100]\) | \(304900096/45125\) | \(33967126082000\) | \([2]\) | \(34560\) | \(1.3210\) | \(\Gamma_0(N)\)-optimal |
14440.l2 | 14440j2 | \([0, -1, 0, 21540, -2614108]\) | \(91765424/296875\) | \(-3575486956000000\) | \([2]\) | \(69120\) | \(1.6676\) |
Rank
sage: E.rank()
The elliptic curves in class 14440.l have rank \(0\).
Complex multiplication
The elliptic curves in class 14440.l do not have complex multiplication.Modular form 14440.2.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.