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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 59850.di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59850.di1 | 59850cd4 | \([1, -1, 0, -2822401692, 57714064299216]\) | \(218289391029690300712901881/306514992000\) | \(3491397330750000000\) | \([2]\) | \(20643840\) | \(3.7230\) | |
| 59850.di2 | 59850cd3 | \([1, -1, 0, -184609692, 813275019216]\) | \(61085713691774408830201/10268551781250000000\) | \(116965222633300781250000000\) | \([2]\) | \(20643840\) | \(3.7230\) | |
| 59850.di3 | 59850cd2 | \([1, -1, 0, -176401692, 901798299216]\) | \(53294746224000958661881/1997017344000000\) | \(22747275684000000000000\) | \([2, 2]\) | \(10321920\) | \(3.3764\) | |
| 59850.di4 | 59850cd1 | \([1, -1, 0, -10513692, 15458715216]\) | \(-11283450590382195961/2530373271552000\) | \(-28822533046272000000000\) | \([2]\) | \(5160960\) | \(3.0298\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 59850.di have rank \(1\).
Complex multiplication
The elliptic curves in class 59850.di do not have complex multiplication.Modular form 59850.2.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 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.
