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SageMath
E = EllipticCurve("er1")
E.isogeny_class()
Elliptic curves in class 102960.er
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.er1 | 102960p1 | \([0, 0, 0, -97435842, 370191316459]\) | \(236807903430715307255728128/16466659495\) | \(7113596901840\) | \([2]\) | \(6451200\) | \(2.8393\) | \(\Gamma_0(N)\)-optimal |
| 102960.er2 | 102960p2 | \([0, 0, 0, -97435647, 370192872286]\) | \(-14800405103160199993360368/123418695914553325\) | \(-853070026161392582400\) | \([2]\) | \(12902400\) | \(3.1859\) |
Rank
sage: E.rank()
The elliptic curves in class 102960.er have rank \(1\).
Complex multiplication
The elliptic curves in class 102960.er do not have complex multiplication.Modular form 102960.2.a.er
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.
