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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 254100i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254100.i2 | 254100i1 | \([0, -1, 0, -249022033, 2076452256562]\) | \(-3856034557002072064/1973796785296875\) | \(-874175351689329292968750000\) | \([2]\) | \(116121600\) | \(3.8743\) | \(\Gamma_0(N)\)-optimal |
| 254100.i1 | 254100i2 | \([0, -1, 0, -4383818908, 111706456600312]\) | \(1314817350433665559504/190690249278375\) | \(1351277634807389173500000000\) | \([2]\) | \(232243200\) | \(4.2208\) |
Rank
sage: E.rank()
The elliptic curves in class 254100i have rank \(1\).
Complex multiplication
The elliptic curves in class 254100i do not have complex multiplication.Modular form 254100.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
