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SageMath
E = EllipticCurve("eq1")
E.isogeny_class()
Elliptic curves in class 102960.eq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.eq1 | 102960bi4 | \([0, 0, 0, -230947707, 1350885672394]\) | \(912446049969377120252018/17177299425\) | \(25645570623129600\) | \([4]\) | \(11010048\) | \(3.1367\) | |
| 102960.eq2 | 102960bi3 | \([0, 0, 0, -15721707, 17118745594]\) | \(287849398425814280018/81784533026485575\) | \(122103653532278751590400\) | \([2]\) | \(11010048\) | \(3.1367\) | |
| 102960.eq3 | 102960bi2 | \([0, 0, 0, -14434707, 21106128994]\) | \(445574312599094932036/61129333175625\) | \(45632802698271360000\) | \([2, 2]\) | \(5505024\) | \(2.7901\) | |
| 102960.eq4 | 102960bi1 | \([0, 0, 0, -822207, 390626494]\) | \(-329381898333928144/162600887109375\) | \(-30345227955900000000\) | \([2]\) | \(2752512\) | \(2.4435\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.eq have rank \(0\).
Complex multiplication
The elliptic curves in class 102960.eq do not have complex multiplication.Modular form 102960.2.a.eq
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
