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SageMath
E = EllipticCurve("em1")
E.isogeny_class()
Elliptic curves in class 114240em
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 114240.ks4 | 114240em1 | \([0, 1, 0, -11585, -1094625]\) | \(-656008386769/1581036975\) | \(-414459356774400\) | \([2]\) | \(393216\) | \(1.4930\) | \(\Gamma_0(N)\)-optimal |
| 114240.ks3 | 114240em2 | \([0, 1, 0, -244865, -46677537]\) | \(6193921595708449/6452105625\) | \(1691380776960000\) | \([2, 2]\) | \(786432\) | \(1.8395\) | |
| 114240.ks2 | 114240em3 | \([0, 1, 0, -305345, -21917025]\) | \(12010404962647729/6166198828125\) | \(1616432025600000000\) | \([2]\) | \(1572864\) | \(2.1861\) | |
| 114240.ks1 | 114240em4 | \([0, 1, 0, -3916865, -2985011937]\) | \(25351269426118370449/27551475\) | \(7222453862400\) | \([2]\) | \(1572864\) | \(2.1861\) |
Rank
sage: E.rank()
The elliptic curves in class 114240em have rank \(0\).
Complex multiplication
The elliptic curves in class 114240em do not have complex multiplication.Modular form 114240.2.a.em
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.
