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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 73920.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.p1 | 73920b6 | \([0, -1, 0, -121702721, -516730924479]\) | \(1520949008089505953959842/278553515625\) | \(36510566400000000\) | \([2]\) | \(4718592\) | \(3.0139\) | |
| 73920.p2 | 73920b4 | \([0, -1, 0, -7607201, -8070277215]\) | \(742879737792994384804/317817082130625\) | \(20828460294512640000\) | \([2, 2]\) | \(2359296\) | \(2.6673\) | |
| 73920.p3 | 73920b5 | \([0, -1, 0, -6419201, -10677462015]\) | \(-223180773010681046402/246754509479287425\) | \(-32342607066469161369600\) | \([2]\) | \(4718592\) | \(3.0139\) | |
| 73920.p4 | 73920b2 | \([0, -1, 0, -550481, -83481519]\) | \(1125982298608534096/467044181552025\) | \(7652051870548377600\) | \([2, 2]\) | \(1179648\) | \(2.3207\) | |
| 73920.p5 | 73920b1 | \([0, -1, 0, -257661, 49517325]\) | \(1847444944806639616/38285567941005\) | \(39204421571589120\) | \([2]\) | \(589824\) | \(1.9741\) | \(\Gamma_0(N)\)-optimal |
| 73920.p6 | 73920b3 | \([0, -1, 0, 1821119, -613296959]\) | \(10191978981888338876/8372623608979245\) | \(-548708260838063800320\) | \([2]\) | \(2359296\) | \(2.6673\) |
Rank
sage: E.rank()
The elliptic curves in class 73920.p have rank \(1\).
Complex multiplication
The elliptic curves in class 73920.p do not have complex multiplication.Modular form 73920.2.a.p
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
