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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 41070l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41070.o2 | 41070l1 | \([1, 0, 1, -114169153, -626489583244]\) | \(-64144540676215729729/28962038218752000\) | \(-74308666316319325421568000\) | \([]\) | \(10834560\) | \(3.6709\) | \(\Gamma_0(N)\)-optimal |
| 41070.o1 | 41070l2 | \([1, 0, 1, -10081365313, -389608204662412]\) | \(-44164307457093068844199489/1823508000000000\) | \(-4678622632622772000000000\) | \([]\) | \(32503680\) | \(4.2202\) |
Rank
sage: E.rank()
The elliptic curves in class 41070l have rank \(1\).
Complex multiplication
The elliptic curves in class 41070l do not have complex multiplication.Modular form 41070.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
