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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 55440di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55440.bv4 | 55440di1 | \([0, 0, 0, -137163, 26175098]\) | \(-95575628340361/43812679680\) | \(-130823960521605120\) | \([2]\) | \(589824\) | \(1.9908\) | \(\Gamma_0(N)\)-optimal |
| 55440.bv3 | 55440di2 | \([0, 0, 0, -2395083, 1426537082]\) | \(508859562767519881/62240270400\) | \(185848451570073600\) | \([2, 2]\) | \(1179648\) | \(2.3374\) | |
| 55440.bv2 | 55440di3 | \([0, 0, 0, -2596683, 1172238842]\) | \(648474704552553481/176469171805080\) | \(526934123503219998720\) | \([2]\) | \(2359296\) | \(2.6840\) | |
| 55440.bv1 | 55440di4 | \([0, 0, 0, -38320203, 91304002298]\) | \(2084105208962185000201/31185000\) | \(93117911040000\) | \([2]\) | \(2359296\) | \(2.6840\) |
Rank
sage: E.rank()
The elliptic curves in class 55440di have rank \(0\).
Complex multiplication
The elliptic curves in class 55440di do not have complex multiplication.Modular form 55440.2.a.di
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
