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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 335040.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 335040.n1 | 335040n1 | \([0, -1, 0, -2907841, 1910735041]\) | \(-10372797669976737841/7632630000000\) | \(-2000848158720000000\) | \([]\) | \(7451136\) | \(2.4457\) | \(\Gamma_0(N)\)-optimal |
| 335040.n2 | 335040n2 | \([0, -1, 0, 11674559, -106044573119]\) | \(671282315177095816559/18919046447754148470\) | \(-4959514512000063496519680\) | \([]\) | \(52157952\) | \(3.4187\) |
Rank
sage: E.rank()
The elliptic curves in class 335040.n have rank \(0\).
Complex multiplication
The elliptic curves in class 335040.n do not have complex multiplication.Modular form 335040.2.a.n
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
